๐ See this first: What came in the RATIONALITY section of the official 2025 paper? (3 min read)
Topic-wise count after reading all 120 questions (12 ร 10) of the RATIONALITY section of MPESB SI Prelims 2025 (exam 16โ21 Jan 2026, 12 shifts):
| Topic | Questions out of 120 | Approx. per shift |
|---|---|---|
| Arithmetic word problems (profit-loss, time-speed, work, average, ratio) โ yes, in the Rationality section! | 39 | 3โ4 |
| Blood Relations | 19 | 1โ2 |
| Order & Ranking | 11 | 1 |
| Direction & Distance | 10 | 1 |
| Coding-Decoding | 8 | 0โ1 |
| Dictionary order / Alphabet test | 8 | 0โ1 |
| Decision Making | 8 | 0โ1 |
| Clock | 7 | 0โ1 |
| Calendar | 7 | 0โ1 |
| Number puzzles (LCM, tyres, heads-legs) | 3 | โ |
Strategy: Topics 1โ9 (below) = the types of all 120 questions of the 2025 Rationality section. Master these first.
Analogy, classification, series, syllogism, Venn, puzzles, data sufficiency and figure questions (mirror, dice, paper folding) appeared in the ANALYTICAL ABILITY section in 2025 (odd-one-out, data sufficiency, floor puzzle and figure analogy came there) โ so study Topics 10โ25 too; they will help in both sections.
Official figure questions (with image options) cannot be reproduced faithfully in text here, so their method + text/SVG examples are given.
Analogy, classification, series, syllogism, Venn, puzzles, data sufficiency and figure questions (mirror, dice, paper folding) appeared in the ANALYTICAL ABILITY section in 2025 (odd-one-out, data sufficiency, floor puzzle and figure analogy came there) โ so study Topics 10โ25 too; they will help in both sections.
Official figure questions (with image options) cannot be reproduced faithfully in text here, so their method + text/SVG examples are given.
โ ๏ธ Special feature of the paper:
- Some official questions also had typos/wrong options (e.g. in one shift the correct ranking answer 25 was not in any option; in one "which is not a leap year" question both 700 and 1800 were non-leap). If you see this in the exam, don't panic โ choose the nearest/intended answer, or leave it (check the negative marking rule in the rulebook).
- The Hindi and English versions sometimes differ โ if in doubt, read the English version.
๐ Jump to Topic (๐ฅ = comes in every shift of the Rationality section):
๐ฅ 1. Blood Relations
๐ฅ 2. Order & Ranking
๐ฅ 3. Direction & Distance
๐ฅ 4. Clock
๐ฅ 5. Calendar
๐ฅ 6. Coding-Decoding
๐ฅ 7. Dictionary Order & Alphabet Test
๐ฅ 8. Decision Making / Course of Action
๐ฅ 9. Arithmetic Questions of Rationality
10. Syllogism
11. Statement-Conclusion / Assumption / Cause-Effect
12. Venn Diagram
13. Analogy
14. Classification (Odd One Out)
15. Series
16. Missing Number
17. Mathematical Operations & Inequality
18. Seating Arrangement
19. Puzzles
20. Data Sufficiency
21. Input-Output
22. Dice & Cube
23. Mirror & Water Images
24. Paper Folding / Cutting
25. Embedded & Counting Figures
๐ 1. Blood Relations (12 min read ยท 18 PYQs)
Concept + Method (4 steps)
- Who is the speaker ("I/my" = the person speaking) and about whom the question asks โ underline both of these first.
- Break the sentence from the back (last): "my mother's father's daughter's son" โ my mother โ her father (my maternal grandfather) โ maternal grandfather's daughter (my mother / maternal aunt) โ her son.
- Draw a family tree: the older generation at the top, children below. Male = โก or (+), Female = โ or (โ), husband-wife = โ, brother-sister = โโ.
- Assume gender only when it is clear from the name/word (father, daughter, brother). Always give the answer as "what the first person is to the second".
Golden Shortcuts for "Only" (asked the most)
| Phrase | Meaning |
|---|---|
| "The only son of my mother / my father" (speaker is male) | = myself |
| "The only daughter of my mother" (speaker is female) | = myself |
| "The only son of my paternal grandfather" | = my father |
| "The only son of my maternal grandfather" | = my maternal uncle |
| "The only daughter of my maternal/paternal grandfather" (only mother fits in the options) | Maternal grandfather's โ mother; paternal grandfather's โ paternal aunt |
| "My father's wife" | = mother (step-mother is not assumed in the exam) |
| "The mother of my son's only daughter" | = daughter-in-law |
| "His brother's father" | = his father |
Relation Vocabulary (Hindi โ English)
| Relation | Whose | Relation | Whose |
|---|---|---|---|
| Paternal grandfather/grandmother (Dada/Dadi) | Father's father/mother | Maternal grandparents (Nana/Nani) | Mother's father/mother |
| Paternal uncle (Chacha/Tau) | Father's younger/elder brother | Maternal uncle (Mama) | Mother's brother |
| Paternal aunt (Bua) ยท her husband (Phupha) | Father's sister ยท her husband | Maternal aunt (Mausi) ยท her husband (Mausa) | Mother's sister ยท her husband |
| Nephew/Niece (Bhatija/Bhatiji) | Brother's son/daughter | Nephew/Niece (Bhanja/Bhanji) | Sister's son/daughter |
| Grandson/Granddaughter (Pota/Poti) | Son's son/daughter | Grandson/Granddaughter (Nati/Natin or Navasa/Navasi) | Daughter's son/daughter |
| Brother/Sister-in-law (Sala/Sali) | Wife's brother/sister | Brother-in-law (Devar/Jeth) ยท Sister-in-law (Nanad) | Husband's younger/elder brother ยท husband's sister |
| Brother-in-law (Jija) | Sister's husband | Sister-in-law (Bhabhi) | Brother's wife |
| Father/Mother-in-law (Sasur/Saas) | Husband's/wife's father/mother | Son-in-law (Damad) ยท Daughter-in-law (Bahu) | Daughter's husband ยท son's wife |
| Cousin = child of a paternal uncle/maternal uncle/paternal aunt/maternal aunt (Chachera, Mamera, Phuphera, Mausera brother-sister). English "Uncle" = both Chacha and Mama; "Aunt" = Bua, Mausi, Chachi, Mami. | |||
Coded Relations (A + B, A ร B type)
The meaning of the symbols is given. Decode one pair at a time from left to right, then connect the first and the last person. Note the gender from every symbol as you go.
Solved Example 1: "The son of her only brother is my wife's brother" โ a man said about a woman. What is the woman to the man?
Step 1: My wife's brother = my brother-in-law (wife's brother).Step 2: Brother-in-law = son of the woman's brother โ the woman's brother = the brother-in-law's father = my father-in-law.
Step 3: Woman = father-in-law's sister = wife's paternal aunt (Bua Saas).
Solved Example 2 (coded): P ร Q = P is the father of Q; P โ Q = P is the sister of Q; P + Q = P is the brother of Q. In "A ร B + C โ D", how is A related to D?
A ร B โ A is B's father. B + C โ B is C's brother (so C is also A's child). C โ D โ C is D's sister (D is also A's child).โด A is D's father. (D's gender is not known โ so saying "D is A's son" would be wrong.)
Solved Example 3: Showing a photo, Ramesh said, "This is the daughter of the only daughter of my mother's husband." What is the girl in the photo to Ramesh?
Mother's husband = father โ father's only daughter = Ramesh's sister (Ramesh himself is male) โ sister's daughter = niece (Bhanji).
โ ๏ธ Exam Traps:
- "Only son" + male speaker = he himself. (The Girish/Abhi PYQs were based on this.)
- A useless person (distractor) is also given โ e.g. in the Chotu PYQ, "Fatu" had no role.
- If gender is not known, do not choose a "son/daughter" option; if the options have "cannot be determined", consider that.
- Reverse question: "relation of A to B" โ "relation of B to A". Re-read the direction of the question.
- In some PYQs, strictly two possibilities arise (e.g. "grandfather's granddaughter" = daughter as well as niece) โ the answer is the only one of these that is in the options.
๐ฏ Official PYQs โ MPESB SI Prelims 2025 (Rationality section)
Q1. Chotu is Motu's brother. Chota is Motu's father. Gotu is Chota's father. Fatu is Gotu's father. How is Gotu related to Chotu? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (3) Grandfather
Chotu and Motu are brothers โ Chota is the father of both โ Gotu (Chota's father) = Chotu's grandfather. Fatu is a distractor.
Chotu and Motu are brothers โ Chota is the father of both โ Gotu (Chota's father) = Chotu's grandfather. Fatu is a distractor.
Q2. Manyak is Arvind's son. Manyak and Kashyap are brothers. Durga is Kashyap's mother. Sanhit is Arvind's brother. Harish is Sanhit's son. What is Harish to Kashyap? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (4) Cousin
Kashyap = Arvind's son; Harish = son of Arvind's brother Sanhit โ paternal cousin brother (cousin).
Kashyap = Arvind's son; Harish = son of Arvind's brother Sanhit โ paternal cousin brother (cousin).
Q3. Introducing a man to her husband, a woman said, "His brother's father is the only son of my grandfather." What is the woman to that man? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (3) Sister
Grandfather's only son = the woman's father. The man's brother's father = the man's father. Both have the same father โ the woman is his sister.
Grandfather's only son = the woman's father. The man's brother's father = the man's father. Both have the same father โ the woman is his sister.
Q4. Looking at old pictures, Geeta pointed to a boy and said, "He is the only son of the only daughter of my grandfather." How is Geeta related to that boy? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) Sister
Grandfather's only daughter = Geeta's mother (this is what fits the options). Mother's only son = Geeta's brother โ Geeta is his sister.
Grandfather's only daughter = Geeta's mother (this is what fits the options). Mother's only son = Geeta's brother โ Geeta is his sister.
Q5. Pointing to a woman, Raghu said, "Her son is my daughter's uncle." What is the woman to Raghu? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (2) Mother
My daughter's uncle = my brother. The woman's son = Raghu's brother โ the woman is Raghu's mother.
My daughter's uncle = my brother. The woman's son = Raghu's brother โ the woman is Raghu's mother.
Q6. Sharda is Surya's granddaughter and Kiran is Surya's only son. What is Sharda's relation to Kiran? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (2) Daughter
Surya's only son is Kiran โ Surya's granddaughter (son's daughter) = Kiran's daughter. Only this is possible in the options.
Surya's only son is Kiran โ Surya's granddaughter (son's daughter) = Kiran's daughter. Only this is possible in the options.
Q7. If M ร N means M is the daughter of N; M รท N means M is the father of N; and M + N means M is the husband of N, then in P ร Q รท R, how is P related to R? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (4) Sister
P ร Q โ P is Q's daughter. Q รท R โ Q is R's father. P and R are both Q's children, P is female โ P is R's sister.
P ร Q โ P is Q's daughter. Q รท R โ Q is R's father. P and R are both Q's children, P is female โ P is R's sister.
Q8. Pahul's mother is the only daughter of Monika's father. How is Monika's husband related to Pahul? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (2) Father
The only daughter of Monika's father = Monika herself โ Monika = Pahul's mother โ Monika's husband = Pahul's father.
The only daughter of Monika's father = Monika herself โ Monika = Pahul's mother โ Monika's husband = Pahul's father.
Q9. Pointing to a digital picture of a boy, Girish said, "He is the son of the only son of my mother." How is Girish related to that boy? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (4) Father
Mother's only son = Girish himself โ the boy is Girish's son โ Girish is his father.
Mother's only son = Girish himself โ the boy is Girish's son โ Girish is his father.
Q10. Making a toast in front of everyone, Kishi said, "I want to dedicate this evening to the woman who is the mother of my son's only daughter." How is the woman related to Kishi? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (4) Daughter-in-law
Mother of son's daughter = son's wife = daughter-in-law (Bahu).
Mother of son's daughter = son's wife = daughter-in-law (Bahu).
Q11. Harsh is telling Kashyap that the girl riding a bicycle in the ground is the daughter of his father's wife. What is Harsh's relation to that girl? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (1) Brother
Father's wife = mother โ mother's daughter = Harsh's sister โ Harsh is her brother.
Father's wife = mother โ mother's daughter = Harsh's sister โ Harsh is her brother.
Q12. If D is R's only brother and R is S's only daughter, how are "D" and "S" related to each other? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (1) Son and father
R is S's daughter and D is R's brother โ D is S's son. S's gender is not given, but in the options only "son and father" (D = son) fits.
R is S's daughter and D is R's brother โ D is S's son. S's gender is not given, but in the options only "son and father" (D = son) fits.
Q13. Pointing to a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (1) Mother
The only daughter of my mother = the woman herself โ she is the man's mother.
The only daughter of my mother = the woman herself โ she is the man's mother.
Q14. Ankit went to his relative's house to meet the only sister of his father's wife. Whom did he go to meet? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (4) Maternal aunt (Mausi)
Father's wife = mother โ mother's sister = maternal aunt.
Father's wife = mother โ mother's sister = maternal aunt.
Q15. X is Y's sister. Z is Y's only son. W is the father of Z's maternal grandmother. How is X related to W? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (2) Granddaughter
Intended chain: Y = Z's mother โ Z's maternal grandmother = Y's mother = X's mother too โ W = father of X's mother โ X is W's granddaughter (daughter's daughter, Natin). In the options, English "Granddaughter" covers both Poti (son's daughter) and Natin (daughter's daughter).
Intended chain: Y = Z's mother โ Z's maternal grandmother = Y's mother = X's mother too โ W = father of X's mother โ X is W's granddaughter (daughter's daughter, Natin). In the options, English "Granddaughter" covers both Poti (son's daughter) and Natin (daughter's daughter).
Q16. Vidya is Vinay's mother. How is the father of Vinay's only sister related to Vidya? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (1) Husband
Father of Vinay's sister = Vinay's father = Vidya's husband.
Father of Vinay's sister = Vinay's father = Vidya's husband.
Q17. Introducing a girl to his friend, Abhi said, "She is the only daughter of the only son of my father." The girl is Abhi's ___: MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (2) Daughter
Father's only son = Abhi himself โ his only daughter = Abhi's daughter.
Father's only son = Abhi himself โ his only daughter = Abhi's daughter.
Q18. Radha is the sister of Suresh's mother. What is Radha's relation to Suresh? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (4) Maternal Aunt (Mausi)
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. A's mother is B's daughter. B's only son is C. What is C to A? Practice MCQ
Answer: (2) Maternal uncle โ A's mother and C are both B's children โ C is the brother of A's mother.
P2. Mohan is Sohan's son. Sohan's sister is Reeta, whose son is Amit. What is Amit to Mohan? Practice MCQ
Answer: (3) Cousin (paternal aunt's son) โ Reeta = Mohan's paternal aunt โ paternal aunt's son = cousin.
P3. Pointing to a woman, a man said, "The son of her only brother is my wife's brother." What is the woman to the man? Practice MCQ
Answer: (3) โ See Solved Example 1 above.
P4. P + Q = P is Q's brother; P โ Q = P is Q's sister; P ร Q = P is Q's father. In "L ร M โ N", what is N's definite relation to L? Practice MCQ
Answer: (3) โ L is M's father; M is N's sister โ N is also L's child, but N's gender is not known.
P5. Reena said, "Rahul is the son of the only son of my maternal grandfather." What is Rahul to Reena? Practice MCQ
Answer: (2) โ Maternal grandfather's only son = maternal uncle โ maternal uncle's son = cousin (Mamera bhai).
๐ 2. Order & Ranking (8 min read ยท 10 PYQs)
Formulas (everything is built from these)
| Situation | Formula |
|---|---|
| One person: L from the left, R from the right | Total = L + R โ 1 |
| Total N, k from the top โ from the bottom? | N โ k + 1 |
| Two persons, counted from opposite ends, x people between them, no overlap | Total = L + R + x |
| Two persons, positions overlap/cross | Total = L + R โ x โ 2 |
| A and B change places (interchange) | A's new position = B's old position (from the same end) |
| Between two people (positions p < q from the same end) | In between = q โ p โ 1 |
Solved Example 1: A is 11th from the left, B is 10th from the right. After changing places, A is 18th from the left. How many in total?
A's new position (18, from the left) = B's old position โ B: 18 from the left, 10 from the right โ Total = 18 + 10 โ 1 = 27. (If "other than A and B" is asked, then 27 โ 2 = 25.)
Solved Example 2 (overlap): A is 10th from the left, B is 12th from the right, and B is to the left of A; there are 3 people between them. Total?
A = 10 (from the left) โ B = 10 โ 4 = 6 (from the left) โ Total = 6 + 12 โ 1 = 17. Formula: 10 + 12 โ 3 โ 2 = 17 โ
Solved Example 3: Out of 52, 15 fail. In the list of those who passed, Samesh is 22nd from the top. From the bottom?
Only 52 โ 15 = 37 in the list โ from the bottom = 37 โ 22 + 1 = 16th.
โ ๏ธ Exam Traps:
- "Other than A and B" / "other than" โ subtract 2 from the total.
- Adding new students at the bottom of the list does not change the rank from the top (the Luno PYQ).
- "4 boys in between" means the difference in positions is 5.
- If both orders (A first or B first) are possible, make both cases โ pick the one in the options; if "minimum" is asked, take the smaller one.
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. Some boys are sitting in a line. P is sitting 14th from the left and Q is 7th from the right. If there are four boys between P and Q, how many boys are there in the line? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (4) 25
No overlap: 14 + 4 + 7 = 25. (Overlap case = 9 + 7 โ 1 = 15, not in the options.)
No overlap: 14 + 4 + 7 = 25. (Overlap case = 9 + 7 โ 1 = 15, not in the options.)
Q2. In a line, 'A' is 11th from the left and 'B' is 10th from the right. If 'A' and 'B' interchange, 'A' becomes 18th from the left. How many more people are there in the line other than 'A' and 'B'? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (3) 25
Total = 18 + 10 โ 1 = 27; other than A, B = 25. (In 18 Jan Shift 1 the same question came with wrong options โ 13/12/7/3.)
Total = 18 + 10 โ 1 = 27; other than A, B = 25. (In 18 Jan Shift 1 the same question came with wrong options โ 13/12/7/3.)
Q3. In a class of 46 students, Shivu is 12th from the top. What will be his position from the bottom? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (2) 35 โ 46 โ 12 + 1 = 35.
Q4. In a line of boys, Ritik is seventh from the left and Anish is twelfth from the right. If they interchange their places, Ritik will be twenty-second from the left. How many boys are there in the line? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (4) 33 โ Anish's old position: 22 from the left, 12 from the right โ 22 + 12 โ 1 = 33.
Q5. In a group of students, Saujanya's rank is 11th from the top and 15th from the bottom. If he is placed 21st from the top, what will be his rank from the bottom? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (1) 5 โ Total = 11 + 15 โ 1 = 25 โ 25 โ 21 + 1 = 5.
Q6. Three persons A, B and C are standing in a queue, not necessarily in the same order. There are 4 persons between A and B and 7 persons between B and C. If there are 11 persons ahead of C and 13 persons behind A, what can be the minimum number of persons in the queue? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (1) 22
C = 12th from the front. B = 12 ยฑ 8 = 4 or 20. A = B ยฑ 5 โ if B = 4 then A = 9 โ Total = 9 + 13 = 22. (With B = 20, A = 15/25 โ Total 28/38, more.) Minimum = 22.
C = 12th from the front. B = 12 ยฑ 8 = 4 or 20. A = B ยฑ 5 โ if B = 4 then A = 9 โ Total = 9 + 13 = 22. (With B = 20, A = 15/25 โ Total 28/38, more.) Minimum = 22.
Q7. In a group of 88 students, Luno's rank is 13th from the top. If 3 new students are added at the bottom of the list, what will be Luno's rank from the top? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (4) 13 โ Adding at the bottom does not change the rank from the top.
Q8. Shivu is sixteenth from the top and forty-ninth from the bottom in a class. How many students are there in the class? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (2) 64 โ 16 + 49 โ 1 = 64.
Q9. In a row of boys, A is 16th from the left end and V is 18th from the right end. G is 11th to the right of A and 3rd from V towards the right end. How many boys are there in the row in total? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (2) 41
G = 16 + 11 = 27th from the left. G is third to the right of V โ V = 24 (from the left). V is 18 from the right โ Total = 24 + 18 โ 1 = 41.
G = 16 + 11 = 27th from the left. G is third to the right of V โ V = 24 (from the left). V is 18 from the right โ Total = 24 + 18 โ 1 = 41.
Q10. In a class of 52 students, 15 students failed. After removing the names of the failed students, a merit list was prepared in which Samesh's position is 22nd from the top. What will be his position from the bottom? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (3) 16th โ 37 โ 22 + 1 = 16.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. In a row of 40 people, Ram is 15th from the left. What is his position from the right? Practice MCQ
Answer: (3) 26 โ 40 โ 15 + 1.
P2. A is 12th from the top, B is 20th from the bottom; A is above B and there are 5 students between them. Total students? Practice MCQ
Answer: (3) 37 โ 12 + 5 + 20.
P3. In a queue, Meena is 9th from the front and 14th from the back. How many people are in the queue? Practice MCQ
Answer: (2) 22 โ 9 + 14 โ 1.
P4. In a row of 30 boys, X is 8th from the left and Y is 10th from the right. How many boys are there between X and Y? Practice MCQ
Answer: (2) 12 โ Y from the left = 30 โ 10 + 1 = 21 โ in between = 21 โ 8 โ 1 = 12.
๐ 3. Direction & Distance (10 min read ยท 10 PYQs)
On paper: up = North, down = South, right = East, left = West
Method: Coordinate (x, y) method โ never goes wrong
- Start = (0, 0). East = +x, West = โx, North = +y, South = โy.
- Add or subtract every walk in x or y. At the end you get (x, y).
- Distance = โ(xยฒ + yยฒ). Direction: x+, y+ โ NE; xโ, y+ โ NW; x+, yโ โ SE; xโ, yโ โ SW; if only x or only y, then a straight direction.
- Turning right = clockwise 90ยฐ; left = anticlockwise 90ยฐ. N โ right = E, E โ right = S, S โ right = W, W โ right = N.
Pythagoras Triplets (save calculation): (3, 4, 5) ยท (6, 8, 10) ยท (5, 12, 13) ยท (8, 15, 17) ยท (7, 24, 25) ยท (9, 12, 15) ยท (12, 16, 20)
Shadow Rules
| Time | Sun | Shadow |
|---|---|---|
| Morning (after sunrise) | East | West |
| Evening (before sunset) | West | East |
Then see whether the shadow is to the person's right/left/front/back. Remember: facing North โ right = East, left = West. Facing South โ right = West, left = East. Facing East โ right = South. Facing West โ right = North.
"In which direction is A from B?"
Take B as the origin (0,0) and see A's position. Don't reverse it โ "In which direction is Q from R" = where Q is when seen from R.
Questions where directions change (SE โ N type)
From the first pair, find how many degrees and in which direction it has turned (N=0ยฐ, NE=45ยฐ, E=90ยฐ, SE=135ยฐ, S=180ยฐ, SW=225ยฐ, W=270ยฐ, NW=315ยฐ). Apply the same turn to the other direction.
Solved Example 1: 5 km East, then turn left and 4 km, then turn left and 8 km. Distance and direction from the start?
East 5 โ (5, 0). Left (North) 4 โ (5, 4). Left (West) 8 โ (โ3, 4). Distance = โ(9 + 16) = 5 km, xโ, y+ โ North-West (NW).
Solved Example 2 (shadow): In the morning, Ravi's shadow was to his left. In which direction is Ravi facing?
Morning shadow = West. West is to his left โ he is facing North (North face โ left = West).
Solved Example 3 (rotation): If North (N) becomes East (E) and East becomes South, what will North-West (NW) become?
N โ E = 90ยฐ clockwise. NW (315ยฐ) + 90ยฐ = 405ยฐ = 45ยฐ = NE.
โ ๏ธ Exam Traps:
- "Walking towards the sun" in the morning = towards East; in the evening = towards West.
- Two people standing face to face: if one faces North, the other faces South.
- Whether "how far" is asked or "how much did he walk in total" โ the two are different (total walk = sum of all distances).
- If the options do not have the direction but the answer comes out SW/NE, look at "none of these".
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. A man walks 2 kilometres towards North. Then he turns East and walks 10 kilometres. After this he turns North and walks 3 kilometres. Then he turns East and walks 2 kilometres. How far is he now from the starting point? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (2) 13 km โ North total 2 + 3 = 5, East total 10 + 2 = 12 โ โ(25 + 144) = 13 (triplet 5-12-13).
Q2. Six houses โ K, L, M, N, O and P โ are located in the same colony. P is 400 metres West of K. M is 200 metres East of L. O is 300 metres North of K. N is 150 metres South of L. L is 250 metres South of K. What is the straight distance between O and N? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (3) 700 m โ K = (0,0). O = (0, 300). L = (0, โ250), N = (0, โ400). O to N = 300 + 400 = 700 m (in the same straight line).
Q3. Y is East of X, which is North of Z. If P is South of Z, in which direction is P from Y? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (4) None of these โ Z = (0,0), X = (0, a), Y = (b, a), P = (0, โc). From Y to P: x decreases, y decreases โ P is South-West of Y, which is not in the options.
Q4. Some boys are sitting in three rows and all are facing North. A is in the middle row. P is just to the right of A but in the same row. Q is just behind P, while R is North of A. In which direction is Q from R? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (4) South-East
R โ front row (North)
A P โ middle row
Q โ back row (South)
From R to Q: down (South) and right (East) โ South-East
Q5. Rasik walked 20 metres towards North. Then he turned right and walked 30 metres. After that he again turned right and walked 35 metres. Then he turned left and walked 15 metres. Finally he again turned left and walked 15 metres. In which direction and how many metres away is he now from the starting point? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (4) 45 m East
N20 โ (0,20); right = E30 โ (30,20); right = S35 โ (30,โ15); left = E15 โ (45,โ15); left = N15 โ (45, 0). โ 45 m East.
N20 โ (0,20); right = E30 โ (30,20); right = S35 โ (30,โ15); left = E15 โ (45,โ15); left = N15 โ (45, 0). โ 45 m East.
Q6. One morning Sujata starts walking towards the sun. After covering some distance she turns right, then turns right again, and after covering some distance she turns right once more. In which direction is she facing now? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (1) North โ Morning sun = East. E โ right S โ right W โ right N.
Q7. One evening before sunset, Rekha and Hema were talking face to face. If Hema's shadow was exactly to Hema's right, in which direction is Rekha facing? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (2) South โ In the evening the shadow is in the East. East is to Hema's right โ Hema is facing North โ Rekha, face to face, faces South.
Q8. Starting from point X, Jayant walked 15 metres towards West. Then he turned left and walked 20 metres. After that he again turned left and walked 15 metres. Then he turned right and walked 12 metres. How far and in which direction is Jayant now from point X? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (1) 32 m, South โ W15 โ (โ15,0); left = S20 โ (โ15,โ20); left = E15 โ (0,โ20); right = S12 โ (0,โ32).
Q9. Town Q is South-East of town P. Town R is South-West of town Q. Town R is South of town P. Town S is West of town R. In which direction is town P with respect to town S? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (4) North East โ P is exactly North of R; S is West of R โ from S to P: up and right = North-East.
Q10. If South-East becomes North, North-East becomes West, and so on, what will West become? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (3) South-East โ SE (135ยฐ) โ N (0ยฐ) = 135ยฐ anticlockwise. Check: NE (45ยฐ) โ 135ยฐ = โ90ยฐ = 270ยฐ = W โ. West (270ยฐ) โ 135ยฐ = 135ยฐ = SE.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. A person walks 8 km towards North, then turns right and walks 6 km. Distance and direction from the starting point? Practice MCQ
Answer: (1) โ (6, 8) โ โ100 = 10, NE.
P2. A person standing facing North turns 90ยฐ clockwise, then 180ยฐ anticlockwise, then 45ยฐ clockwise. Which way is he facing now? Practice MCQ
Answer: (2) โ N โ E โ W โ (45ยฐ clockwise from W) NW.
P3. In the evening, Mohan's shadow was exactly behind him. Which way is he facing? Practice MCQ
Answer: (2) West โ In the evening the shadow is in the East; East is behind โ facing West (towards the sun).
P4. A is 10 m South of B. C is 24 m East of A. What is the straight distance between B and C? Practice MCQ
Answer: (2) 26 m โ โ(10ยฒ + 24ยฒ) = โ676 = 26 (double of 5-12-13).
๐ 4. Clock (10 min read ยท 7 PYQs)
Basic Facts
| Fact | Value |
|---|---|
| Speed of the minute hand | 6ยฐ per minute (360ยฐ / 60 min) |
| Speed of the hour hand | 0.5ยฐ per minute = 30ยฐ per hour |
| Relative difference between the two | 5.5ยฐ per minute |
| Between two numbers (e.g. 12 and 1) | 30ยฐ (5 minute spaces) |
Angle Formula: ฮธ = | 30H โ 5.5M | (H = hour, M = minute). If ฮธ > 180ยฐ, take 360ยฐ โ ฮธ (the smaller angle).
Hands coincide (0ยฐ) between H and H+1: M = 60H/11 โ e.g. between 4 and 5 at 240/11 = 219โ11 minutes.
Hands opposite (180ยฐ): find M from 5.5M = 30H ยฑ 180.
Right angle (90ยฐ): find M from 5.5M = 30H ยฑ 90 (twice every hour โ with a few exceptions).
Hands coincide (0ยฐ) between H and H+1: M = 60H/11 โ e.g. between 4 and 5 at 240/11 = 219โ11 minutes.
Hands opposite (180ยฐ): find M from 5.5M = 30H ยฑ 180.
Right angle (90ยฐ): find M from 5.5M = 30H ยฑ 90 (twice every hour โ with a few exceptions).
| How many times? | In 12 hours | In 24 hours (1 day) |
|---|---|---|
| Hands coincide | 11 | 22 |
| Hands opposite in a line (180ยฐ) | 11 | 22 |
| Hands in a straight line (0ยฐ or 180ยฐ) | 22 | 44 |
| Right angle (90ยฐ) | 22 | 44 |
In a correct clock, the hands meet every 655โ11 minutes. If in some clock they meet every 65 minutes, that clock is running fast.
How much has the hour hand turned?
Time difference (minutes) ร 0.5ยฐ. E.g. 12:00 to 7:10 = 430 min ร 0.5 = 215ยฐ.
Fast/Slow Clock (Gain/Loss) Method
- Find how much the clock is behind/ahead at the first time and how much ahead/behind at the second time โ the total change (if behind โ ahead, add them).
- Find the total hours between the two times.
- The correct time will be when the initial difference is wiped out: time = (total hours ร initial difference) รท total change.
Solved Example 1: Angle at 2:30?
|30ร2 โ 5.5ร30| = |60 โ 165| = 105ยฐ.
Solved Example 2: Between 4 and 5, when will the hands be in opposite directions?
5.5M โ 120 = 180 โ M = 300/5.5 = 546โ11 minutes past 4 o'clock.
Solved Example 3: A clock is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 pm on Thursday. When did it show the correct time?
Total change = 1 + 2 = 3 minutes, in 48 hours. To correct 1 minute = 48 ร 1/3 = 16 hours โ Tuesday 1 pm + 16 h = Wednesday 5 am.
โ ๏ธ Exam Traps:
- At 8:30 the hour hand is not on 8, but between 8 and 9 โ so the answer is 75ยฐ, not 60ยฐ.
- For "how many degrees has the hour hand turned", use only 30ยฐ per hour; not the formula |30H โ 5.5M|.
- Clock questions with mirror/water images โ see Topic 23.
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. When the time is 8.30, the angle between the minute hand and the hour hand of a clock will be: MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (2) 75ยฐ โ |240 โ 165| = 75ยฐ.
Q2. A clock that runs uniformly is 2 minutes slow at noon on Monday and 4 minutes 48 seconds fast at 2 pm on the next Monday. When was it correct? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (2) 2 pm on Wednesday
Monday 12 noon to next Monday 2 pm = 7ร24 + 2 = 170 hours. Total change = 2 + 4.8 = 6.8 minutes. To correct 2 minutes = 170 ร 2/6.8 = 50 hours โ Monday noon + 50 h = Wednesday 2 pm.
Monday 12 noon to next Monday 2 pm = 7ร24 + 2 = 170 hours. Total change = 2 + 4.8 = 6.8 minutes. To correct 2 minutes = 170 ร 2/6.8 = 50 hours โ Monday noon + 50 h = Wednesday 2 pm.
Q3. Henry started a journey between 8 am and 9 am, when the hands of the clock were together. He reached his destination between 2 pm and 3 pm, when the hands of the clock were exactly 180ยฐ apart. How long did he travel? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (2) 6 hours
Coinciding between 8โ9: M = 480/11 = 437โ11 โ 8:437โ11. Between 2โ3 at 180ยฐ: 5.5M = 60 + 180 โ M = 437โ11 โ 2:437โ11. Difference = exactly 6 hours.
Coinciding between 8โ9: M = 480/11 = 437โ11 โ 8:437โ11. Between 2โ3 at 180ยฐ: 5.5M = 60 + 180 โ M = 437โ11 โ 2:437โ11. Difference = exactly 6 hours.
Q4. At 3:40, the hour hand and the minute hand of a clock make an angle of ______. MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (3) 130ยฐ โ |90 โ 220| = 130ยฐ.
Q5. A clock shows the correct time at 8 in the morning. When the clock shows 2 in the afternoon, through how many degrees will the hour hand have turned? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (4) 180ยฐ โ 6 hours ร 30ยฐ = 180ยฐ.
Q6. A clock is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 pm on Thursday. When did it show the correct time? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (4) 5 am on Wednesday โ Solved Example 3 above.
Q7. A clock starts at 12 noon; at 10 minutes past 7, through how many degrees has the hour hand turned? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (4) 215ยฐ โ 430 minutes ร 0.5ยฐ = 215ยฐ.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Angle between the hands at 20 minutes past 7? Practice MCQ
Answer: (2) 100ยฐ โ |210 โ 110|.
P2. Angle at 9:15? Practice MCQ
Answer: (1) 172.5ยฐ โ |270 โ 82.5| = 187.5 โ smaller angle 360 โ 187.5 = 172.5ยฐ.
P3. In a day (24 hours), how many times do the hands of a clock form a right angle? Practice MCQ
Answer: (3) 44
P4. When will the hands meet between 3 and 4 o'clock? Practice MCQ
Answer: (2) โ M = 60ร3/11 = 180/11 = 164โ11.
๐ 5. Calendar (10 min read ยท 6 PYQs)
Odd Days โ the complete concept
The remainder left after dividing by 7 = odd days. The same weekday returns after every 7 days.
| Period | Odd days |
|---|---|
| Ordinary year (365 days) | 1 |
| Leap year (366 days) | 2 |
| 100 years | 5 |
| 200 years | 3 |
| 300 years | 1 |
| 400 years (and 800, 1200, 1600, 2000) | 0 |
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Odd days | 3 | 0 (leap: 1) | 3 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 |
Day code: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.
Leap year rule: If the year is divisible by 4 โ leap. But a century year (multiple of 100) is leap only if it is divisible by 400.
โ Leap: 1600, 2000, 2400, 800, 1200, 2024 ยท โ Not leap: 700, 1800, 1900, 2100, 2026
On the same date next year: weekday moves +1; if 29 Feb comes in between, +2.
On the same date last year: weekday โ1; if 29 Feb is in between, โ2.
โ Leap: 1600, 2000, 2400, 800, 1200, 2024 ยท โ Not leap: 700, 1800, 1900, 2100, 2026
On the same date next year: weekday moves +1; if 29 Feb comes in between, +2.
On the same date last year: weekday โ1; if 29 Feb is in between, โ2.
Weekday of any date (Method)
- Odd days of the previous complete years: centuries (multiple of 400 = 0) + remaining years (ordinary ร 1 + leap ร 2).
- Odd days of the complete months of that year + the given date.
- Total รท 7 โ remainder = day code.
Solved Example 1: What day was 15 August 1947?
Up to 1946: 1600 years โ 0; next 300 โ 1; next 46 years (1901โ1946) have 11 leap + 35 ordinary = 22 + 35 = 57 โ 57 รท 7 remainder 1. Total = 0 + 1 + 1 = 2.In 1947: Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + Jun 2 + Jul 3 + 15 (Aug) = 31 โ remainder 3.
Total = 2 + 3 = 5 โ Friday โ
Solved Example 2: What day was 26 January 1950?
Up to 1949: 1600 โ 0, 300 โ 1, 49 years (1901โ1949): 12 leap + 37 ordinary = 24 + 37 = 61 โ remainder 5. 1950: 26 โ remainder 5. Total = 0 + 1 + 5 + 5 = 11 โ remainder 4 โ Thursday โ
Solved Example 3: 1 January 2026 was a Thursday. What about 1 January 2027?
2026 is an ordinary year โ +1 โ Friday. (Exam date 28 Oct 2026 = Wednesday.)
Other important Facts
- A weekday 53 times: an ordinary year has 52 weeks + 1 day โ probability of it coming 53 times is 1/7; a leap year has 52 weeks + 2 days โ 2/7.
- Calendar repeat: a leap year's calendar repeats after 28 years (e.g. 2024 โ 2052); the year after a leap year after 6 years (2025 โ 2031); the other two years after 11 years (2026 โ 2037, 2023 โ 2034). (This can change if a non-leap century year comes in between.)
- The last day of a century (31 Dec 1900/2000...) can only be Monday, Wednesday, Friday or Sunday โ never Tuesday, Thursday or Saturday.
- "If yesterday were tomorrow, today would be Friday" type: real today = T. Treat yesterday (T โ 1) as "tomorrow" โ then "today" = T โ 2 = Friday โ T = Sunday.
โ ๏ธ Exam Traps:
- 1800, 1900, 700 are not leap years (not divisible by 400). 2000, 1200, 800 are leap years.
- 20 March 1991 โ 20 March 1992: 29 Feb 1992 comes in between โ +2 (not just +1).
- 8 Feb 2004 โ 8 Feb 2005: 29 Feb 2004 comes in between โ โ2.
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. 20 March 1991 was a Wednesday. Which day of the week was 20 March 1992? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (3) Friday โ 29 Feb 1992 in between โ 366 days โ +2 โ Wednesday + 2 = Friday.
Q2. What is the probability of 53 Mondays in an ordinary year? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (2) 1/7 โ 1 extra day; out of 7 days, 1 is Monday.
Q3. 8 February 2005 was a Tuesday. Which day of the week was 8 February 2004? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (3) Sunday โ 29 Feb 2004 in between โ โ2 โ Sunday.
Q4. What day was 10 June 2002? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (2) Monday
Up to 2001: 2000 years โ 0; 2001 โ 1. 2002: Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + 10 = 21 โ 0. Total = 1 โ Monday.
Up to 2001: 2000 years โ 0; 2001 โ 1. 2002: Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + 10 = 21 โ 0. Total = 1 โ Monday.
Q5. What is the probability of 53 Tuesdays in a leap year? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (3) 2/7 โ The 2 extra days can form 7 pairs (Sun-Mon, Mon-Tue, ..., Sat-Sun); 2 of them contain Tuesday.
Q6. Your friend said, "If yesterday were tomorrow, today would be Friday." On which day did your friend say this? (English: "If yesterday was tomorrow, today would be Friday.") MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (1) Sunday โ If yesterday (T โ 1) were "tomorrow", then "today" = T โ 2 = Friday โ T = Sunday.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Which of these is a leap year? Practice MCQ
Answer: (3) 2000 โ divisible by 400.
P2. 1 January 2001 was a Monday. What day was 1 January 2000? Practice MCQ
Answer: (2) Saturday โ 2000 is leap (29 Feb 2000 in between) โ โ2.
P3. In which year will the calendar of 2026 be used again exactly? Practice MCQ
Answer: (2) 2037
P4. The 3rd of a month is a Monday. What day will the 24th of the same month be? Practice MCQ
Answer: (1) Monday โ 24 โ 3 = 21 days = exactly 3 weeks.
๐ 6. Coding-Decoding (10 min read ยท 8 PYQs)
Alphabet Positions (worth memorising)
A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13
N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26
Reverse order (reverse position) = 27 โ position (e.g. D: 27 โ 4 = 23)
EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25 โ count from the nearest of these (e.g. R = T โ 2 = 18).
Opposite letters (sum = 27): AโZ, BโY, CโX, DโW, EโV, FโU, GโT, HโS, IโR, JโQ, KโP, LโO, MโN.
To remember: AZad, BoY, DeW, GT road, HS (High School), IR (Indian Railway), KP, LOve, MN.
Opposite letters (sum = 27): AโZ, BโY, CโX, DโW, EโV, FโU, GโT, HโS, IโR, JโQ, KโP, LโO, MโN.
To remember: AZad, BoY, DeW, GT road, HS (High School), IR (Indian Railway), KP, LOve, MN.
Main types of Coding
| Type | How to identify | Example |
|---|---|---|
| Letter shift (+n / โn) | Every letter moves equally forward/backward | NIGHT โ OJHIU (+1) |
| Increasing shift | +1, +2, +3... or โ1, โ2, โ3... | DELHI โ CCIDD (โ1, โ2, โ3, โ4, โ5) |
| Opposite letter | Each letter's pair (sum 27) | COLD โ XLOW |
| Reverse / writing backwards | Word from the back | PENCIL โ LICNEP |
| Letter โ number | Position or a digit for some letter | EXAM โ 5X1M (E = 5, A = 1, the rest as they are) |
| Digit substitution | One digit for each letter | DELHI = 45189 โ D4 E5 L1 H8 I9 |
| Sum coding | Sum of positions | CAT = 3 + 1 + 20 = 24 |
| Shift + swap (mixed) | After the shift, some letters change places | FRIEND โ EQHDCM (โ1, then the last two letters swapped with each other) |
| Sentence / word coding | Common word in two sentences = common code | Example below |
Solved Example 1: If DELHI is written as CCIDD, how is BOMBAY written?
Dโ1 = C, Eโ2 = C, Lโ3 = I, Hโ4 = D, Iโ5 = D. In the same way: Bโ1 = A, Oโ2 = M, Mโ3 = J, Bโ4 = X (behind A come Z, Y, X โ wrap around), Aโ5 = V, Yโ6 = S โ AMJXVS.
Solved Example 2 (word coding): 'tom ka pa' = 'eat sweet fruits'; 'ka ja ra' = 'fruits are good'; 'ja ma na' = 'good for health'. Code for 'good'?
Common word in sentences 1 and 2 is 'fruits' and the common code is 'ka' โ fruits = ka. Common word in sentences 2 and 3 is 'good' and the common code is 'ja' โ good = ja. The rest: are = ra.
Solved Example 3: If CAT = 24, then DOG = ?
C3 + A1 + T20 = 24 (sum of positions). DOG = 4 + 15 + 7 = 26.
โ ๏ธ Exam Traps:
- Don't decide the pattern from only the first 2 letters โ check the whole word (in the FRIEND PYQ the last two letters were swapped).
- After Z, go back to A (wrap around): Y + 3 = B.
- Options differ by one letter at a time โ don't choose by matching only the first and last letters.
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. If DELHI is written as 45189, find the code for HELD. MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (2) 8514 โ D4 E5 L1 H8 I9 โ H8 E5 L1 D4.
Q2. If in a code EXAM is written as 5X1M, how will TEST be written? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1
Correct answer: (1) 20E19T โ 1st and 3rd letters โ position number; 2nd and 4th stay as they are. T = 20, E, S = 19, T.
Q3. In a code, NIGHT = OJHIU. Using the same assignment, how is DAYLIGHT coded? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (1) EBZMJHIU โ every letter +1.
Q4. If ENGLISH is written as FOHMJTI, find the code for HINDI. MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (4) IJOEJ โ +1: HโI, IโJ, NโO, DโE, IโJ.
Q5. If COUNTRY is coded as DPVOUSZ, what will NATION be in the same code? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (2) OBUJPO โ +1.
Q6. If DOCTOR is coded as GRFWRU, find the code for ENGINEER. MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (3) HQJLQHHU โ +3: EโH, NโQ, GโJ, IโL, NโQ, EโH, EโH, RโU.
Q7. If "CAPITAL" is coded as "DBQJUBM", how will "CURRENCY" be coded? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (4) DVSSFODZ โ +1.
Q8. In a certain code, FRIEND is written as EQHDCM. Using the same code, how will FAMILY be written? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (2) EZLHXK
FRIEND โ1 = E Q H D M C, then swap the last two letters โ EQHDCM โ. FAMILY โ1 = E Z L H K X โ swap โ EZLHXK.
FRIEND โ1 = E Q H D M C, then swap the last two letters โ EQHDCM โ. FAMILY โ1 = E Z L H K X โ swap โ EZLHXK.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. DELHI โ CCIDD, then BOMBAY โ ? Practice MCQ
Answer: (1) AMJXVS โ Solved Example 1.
P2. COLD โ XLOW, then HEAT โ ? Practice MCQ
Answer: (1) SVZG โ Opposite letters: HโS, EโV, AโZ, TโG.
P3. If PEN = 35 (sum of positions), then INK = ? Practice MCQ
Answer: (2) 34 โ P16 + E5 + N14 = 35 โ; I9 + N14 + K11 = 34.
P4. If MOTHER is written as OQVJGT, then SISTER = ? Practice MCQ
Answer: (1) UKUVGT โ +2: SโU, IโK, SโU, TโV, EโG, RโT.
P5. 'sky is blue' = 'la mo ti'; 'blue is colour' = 'mo ti ra'; 'colour of sky' = 'ra la su'. Code for 'of'? Practice MCQ
Answer: (3) su โ blue/is = mo/ti; colour = ra (sentences 2 and 3); sky = la (sentences 1 and 3) โ of = su.
๐ 7. Dictionary Order & Alphabet Test (7 min read ยท 8 PYQs)
Dictionary Order Rules
- Compare the first letter; if equal, the second, then the third... wherever the first difference comes, that decides.
- If one word is the starting part (prefix) of another, the shorter word comes first: Gad < Gadfly; Dwell < Dwelling < Dwellings.
- Not the length of letters but the order matters: Type (type) < Typhoon (typh) < Typical (typi) < Tyrant (tyr).
Solved Example: Cling, Clinic, Clinker, Clip, Climax โ arrange in order.
Climax (m) < Cling... now the 5th letter in Cling / Clinic / Clinker: cling < clinic < clinker. In Clip the 4th letter is p (after n).Order: Climax, Cling, Clinic, Clinker, Clip โ Clinic comes after Cling.
Alphabet Test Formulas
| Question | Formula |
|---|---|
| k-th letter from the left | Position k |
| k-th letter from the right | Position 27 โ k |
| m-th to the right of the k-th letter from the left | k + m |
| m-th to the left of the k-th letter from the right | 27 โ k โ m |
| Letter exactly midway between two letters (positions p, q) | (p + q) รท 2 |
Solved Example: Which is the 5th letter to the left of the 8th letter from the right?
8th from the right = 27 โ 8 = 19 (S). 5th to its left = 19 โ 5 = 14 = N.
Solved Example: Which word cannot be formed from the letters of the word "POLICE" โ PILE, LICE, POLE, SLICE?
SLICE has S, which is not in POLICE โ SLICE.
โ ๏ธ Exam Traps:
- "Comes after" = only the immediately next word (from the options), not the very last one.
- A plural (Dwellings) comes right after its singular (Dwelling).
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. Which word comes after 'Dwell' in an English dictionary? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (2) Dwelling โ Order: Dwarf, Dwell, Dwelling, Dwellings, Dwindle.
Q2. Which word comes after "Cling" in an English dictionary? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (2) Clinic โ Solved Example above.
Q3. Which word comes first in an English dictionary? "Quilt", "Quip", "Quirk", "Quick" MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (4) Quick โ quic < quil < quip < quir.
Q4. Which word comes last in an English dictionary? "Fiction", "Fiddle", "Field", "Fiend" MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (1) Fiend โ fic < fid < fiel < fien.
Q5. Which word comes first in an English dictionary? "Crucial", "Crude", "Cruise", "Crumb" MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (1) Crucial โ cruc < crud < crui < crum.
Q6. If 21 letters are counted from the end of the English alphabet and 20 letters are counted from the beginning, which letter will come exactly in the middle of the sequence so formed? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (4) M โ 21st from the end = 27 โ 21 = 6 (F); 20th from the beginning = T (20). Sequence from F to T โ middle letter = (6 + 20)/2 = 13 = M.
Q7. Which word comes first in an English dictionary? "Gadget", "Gadfly", "Gadgets", "Gad" MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (2) Gad โ the shorter prefix word comes first: Gad, Gadfly, Gadget, Gadgets.
Q8. Which word comes first in an English dictionary? "Tyrant", "Typhoon", "Type", "Typical" MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (1) Type โ type < typh < typi < tyr.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Which will be the third word in the dictionary? Beach, Bench, Beast, Beard Practice MCQ
Answer: (3) Beast โ Beach (beac), Beard (bear), Beast (beas), Bench (ben).
P2. 6th letter to the right of the 10th letter from the left? Practice MCQ
Answer: (1) P โ 10 + 6 = 16.
P3. Which is the 12th letter from the right? Practice MCQ
Answer: (2) O โ 27 โ 12 = 15.
P4. Which word cannot be formed from the letters of "DEPARTMENT"? Practice MCQ
Answer: (4) PARROT โ DEPARTMENT has no O and has R only once. (The two E's of TEMPER are also present in DEPARTMENT.)
P5. Which word cannot be formed from the letters of "EDUCATION"? Practice MCQ
Answer: (3) NATION โ NATION needs N twice; EDUCATION has N only once.
๐ 8. Decision Making & Course of Action (7 min read ยท 7 + 2 PYQs)
6 rules for choosing the right option (think like a Police officer)
- Safe โ safety of yourself and others first (walking alone on an unsafe route at night โ, a safe cab โ).
- Legal/Ethical โ breaking rules, bribery, lying, making a photo viral โ.
- Direct effect on the problem โ the measure that reduces the problem directly and quickly (malnutrition โ free meals and cheap ration).
- Talk / consult โ mediation in a conflict, talk to the family in a family decision, ask the manager about priority when there are two urgent tasks.
- Extreme option โ โ hunger strike, refusing/resigning immediately, selling the vehicle, leaving without informing.
- Ignoring โ โ "it will get fixed on its own" is almost never right.
Course of Action (statement + action): An action "follows" only when it (i) solves/reduces the problem, (ii) is practical, and (iii) is not harsher than needed. "Shut everything down / punish everyone" type = โ.
Solved Example: Statement: Many people in the city got dengue. Actions: I. The municipal corporation should do fogging and run a drive to remove stagnant water. II. All people of the city should be banned from leaving their homes.
I is a practical step at the root of the problem (mosquitoes) โ. II is extreme and impractical โ โ only I.
๐ฏ Official PYQs โ MPESB SI Prelims 2025
Q1. You miss the last train and still have to reach home safely. What will be the best decision? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Rationality)
Correct answer: (4) Take a safe cab/ride
Q2. Petroleum prices have been raised twice in the last one month. The middle class is struggling under the pressure of inflation. What measure do you suggest? What should they do? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (2) Reduce the use of private vehicles โ practical, in their own hands; (3) and (4) are extreme.
Q3. Two team members are in conflict with each other and it is affecting the work. As team lead, what will be your best step? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (1) Mediation
Q4. You are the chairperson of a committee examining the health condition of poor children. You find that a large number of children are malnourished. What will be the very first step you take to reverse this trend? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (2) โ "First step" = direct and immediate effect (immediate nutrition for children). Jobs/education are slow, tax is indirect.
Q5. You are working on a deadline but you get an urgent call from your family. What will be the best decision? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (1)
Q6. You have been offered a job with a higher salary, but the transfer will affect your family. What should be the best next step? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (3)
Q7. If you get two urgent tasks from two different managers at the same time, what will be the best approach? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (1)
Q8. A student is struggling with time management for an upcoming entrance exam. What will be the most effective decision to solve this problem? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Analytical Ability)
Correct answer: (2)
Q9. You are leading a team that is facing a tight deadline. A team member suggests a shortcut that may save time but may compromise quality. What should you do? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Analytical Ability)
Correct answer: (3) โ balanced: decide after understanding the risk.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. On duty you find an injured person on the road; the crowd is only making videos. Best step? Practice MCQ
Answer: (2) โ saving life is the first priority.
P2. Statement: Many cases of cheating were caught in an exam. Actions: I. Surveillance (CCTV/flying squad) should be increased at exam centres. II. All exams should be cancelled forever. Practice MCQ
Answer: (1) Only I โ II is extreme.
P3. You see your colleague taking a bribe. Most appropriate step? Practice MCQ
Answer: (3)
๐ 9. Arithmetic Questions of the Rationality Section (Profit-Loss, Speed, Work, Average...) (15 min read ยท 39 PYQs)
In 2025, 39 of the 120 Rationality questions were direct arithmetic. The full concept is in the Mathematics notes; here only the essential formulas + all official questions with solutions.
Formula Recap (at a glance)
| Topic | Formula / Trick |
|---|---|
| Profit / Loss | SP = CP ร (100 ยฑ %)/100 ยท CP = SP ร 100/(100 ยฑ %) ยท Profit% = (Profit/CP) ร 100 |
| SPs given for x% profit and x% loss (equal %) | CP = average of the two SPs: (SPโ + SPโ)/2 |
| Price rises by r%, keep expenditure the same | Reduce consumption = r/(100 + r) ร 100 % |
| km/h โ m/s | ร 5/18 (km/h โ m/s) ยท ร 18/5 (m/s โ km/h) |
| Equal distance, two speeds x, y | Average speed = 2xy/(x + y) |
| Moving towards each other | Time = distance รท (speedโ + speedโ) |
| Stoppage per hour | (speed without stoppage โ speed with stoppage)/speed without stoppage ร 60 minutes |
| Ratio of speeds a : b : c | Ratio of times = 1/a : 1/b : 1/c |
| Work | 1 day's work = 1/days; together = add; MโDโ = MโDโ |
| Partnership | Ratio of profit = capital ร time |
| Average | Total = average ร number |
| Mixture profit | Find total CP and total SP, then profit% |
โ ๏ธ Exam Traps:
- Some official options had typos (e.g. height "166 m" = 166 cm; "1.57" = 157%). Identify the correct value and choose the option.
- If "approximately" is written, do the full calculation and take the nearest option.
- "Loss equal to x" type: SP = CP of (total โ x) items.
๐ฏ Official PYQs โ MPESB SI Prelims 2025 (Rationality section)
Q1. On selling 17 balls for 720 rupees, there is a loss equal to the cost price of 5 balls. The cost price of one ball is: MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (4) โน60 โ SP(17) = CP(17) โ CP(5) = CP(12) = 720 โ CP = 60.
Q2. If Farheen travels at 7/11 of her usual speed, the time taken to cover the same distance will be what percent of the usual time? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 2
Correct answer: (1) 1.57 โ Speed 7/11 times โ time 11/7 = 1.571 times (โ 157%). The options were printed as ratios.
Q3. A seller bought 6 toffees for one rupee. How many toffees should he sell for one rupee to earn a 20% profit? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (3) 5 โ CP of 6 toffees โน1 โ at 20% profit, SP of 6 toffees โน1.20 โ for โน1, 6/1.2 = 5.
Q4. The manager of an electronics store charges his customer 11% more than the cost price. If a customer paid โน1,33,200 for an LED TV, what was the original price of the TV? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (1) โน1,20,000 โ 133200 ร 100/111 = 120000.
Q5. One person's speed is 33.12 km/h and another person's speed is 8.8 m/s. If the distance between them is 27 metres and they are moving towards each other, how much time will they take to meet? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 1
Correct answer: (2) 1.5 seconds โ 33.12 ร 5/18 = 9.2 m/s; total 9.2 + 8.8 = 18 m/s โ 27/18 = 1.5 s.
Q6. In a certain shop, the profit is 320% of the cost price. If the cost price increases by 25% but the selling price remains constant, the profit will be approximately what percent of the selling price? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (2) 70% โ CP 100 โ SP 420. New CP 125 โ profit 295 โ 295/420 = 70.2% โ 70%.
Q7. The average height of 40 students in a class is 165 cm. If the average height of the 15 girls is 160 cm, what will be the average height of the boys? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (2) 168 (the "m" in the options is a typo, read cm) โ total 6600 โ 2400 = 4200; 25 boys โ 168.
Q8. There are two exam rooms A and B. If 10 students are sent from A to B, the number of students in both rooms becomes equal. If 20 students are sent from B to A, the number of students in room A becomes double the number in room B. What is the number of students in room A? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) 100 โ A โ 10 = B + 10 โ A = B + 20. A + 20 = 2(B โ 20) โ B + 40 = 2B โ 40 โ B = 80, A = 100.
Q9. One-third of Rahul's savings in National Savings Certificate is equal to half of his savings in Public Provident Fund. If his total savings are โน1,50,000, how much has he saved in Public Provident Fund? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) โน60,000 โ NSC/3 = PPF/2 โ NSC : PPF = 3 : 2 โ PPF = 2/5 ร 150000 = 60000.
Q10. In a joint business, A invested โน2000 for 12 months and B invested โนX for 8 months. If B receives โน4000 out of a total annual profit of โน10,000, find the value of X. MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (2) 2000 โ A : B = 6000 : 4000 = 3 : 2 = 24000 : 8X โ 8X = 16000 โ X = 2000.
Q11. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B, 75 km away, at the same time. On the way, the train lost about 12.5 minutes while stopping at stations. What is the speed of the car? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) 120 โ 75/x โ 75/(1.5x) = 12.5/60 โ 25/x = 5/24 โ x = 120.
Q12. On a journey, a person covers the first 160 km at a speed of 64 km/h and the next 160 km at a speed of 80 km/h. What will be the average speed for the first 320 km of the journey? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) 71.11 km/h โ 2 ร 64 ร 80/144 = 71.11.
Q13. A journey of 600 kilometres is completed in 8 hours if 120 kilometres are covered by train and the rest by car. If 200 kilometres are covered by train and the rest by car, the journey takes 20 minutes more. What is the ratio of the speed of the train to the speed of the car? MPESB SI Prelims 2025 โ 17 Jan 2026, Shift 2
Correct answer: (3) 3:4 โ 120/t + 480/c = 8 and 200/t + 400/c = 25/3. Solving gives t = 60, c = 80 โ 3 : 4. (Check: 2 + 6 = 8 โ; 3.33 + 5 = 8.33 โ)
Q14. A woman buys a bicycle for โน1400 and sells it at a loss of 15%. What will be the selling price of the bicycle? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (3) โน1190 โ 1400 ร 0.85.
Q15. A trader mixes 26 kg of rice at โน20 per kg with 30 kg of another variety of rice at โน36 per kg and sells the mixture at โน30 per kg. What is his profit percentage? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (2) 5% โ CP = 520 + 1080 = 1600; SP = 56 ร 30 = 1680 โ 80/1600 = 5%.
Q16. Jeevit sold a bicycle for โน2100 and incurred a loss of 25% on it. If he wants to earn a profit of 15%, at what price should he sell the bicycle? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (3) โน3220 โ CP = 2100/0.75 = 2800 โ 2800 ร 1.15 = 3220.
Q17. Jishor crosses a 600-metre-long road in 5 minutes. What will be his speed in kilometres per hour? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (2) 7.2 โ 600 m/300 s = 2 m/s ร 18/5 = 7.2 km/h.
Q18. A can do a job in 4 hours, B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How much time will B alone take to do it? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (3) 12 hours โ C = 1/2 โ 1/4 = 1/4; B = 1/3 โ 1/4 = 1/12.
Q19. 10 women can complete a job in 7 days and 10 children take 14 days to complete the same job. How many days will 5 women and 10 children take to complete the job? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (3) 7 โ 5 women = 1/14 per day; 10 children = 1/14 โ total 1/7 โ 7 days.
Q20. P can do a job in 10 days and Q can do the same job in 15 days. If they work on alternate days, starting with P, in how many days will the work be completed? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 1
Correct answer: (2) 12 days โ in 2 days 1/10 + 1/15 = 1/6 โ in 12 days exactly 6/6 = complete.
Q21. Sam bought 20 dozen toys at โน375 per dozen. He sold each of them at โน33. What was his percentage profit? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (3) 5.6% โ SP per dozen = 33 ร 12 = 396; profit 21/375 = 5.6%.
Q22. If a โ b = 3 and aยฒ + bยฒ = 29, find the value of ab. MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (1) 10 โ (a โ b)ยฒ = aยฒ + bยฒ โ 2ab โ 9 = 29 โ 2ab โ ab = 10.
Q23. Excluding stoppages, the speed of a bus is 54 km/h and including stoppages its speed is 45 km/h. For how many minutes does the bus stop per hour? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (2) 10 โ 9/54 ร 60 = 10 minutes.
Q24. A, B and C can do a job in 20, 30 and 60 days respectively. If B and C help him every third day, in how many days can A do the job? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (2) 15 days โ in 3 days: 2/20 + (1/20 + 1/30 + 1/60) = 1/10 + 1/10 = 1/5 โ 15 days.
Q25. 4 men and 6 women can complete a job in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it? MPESB SI Prelims 2025 โ 18 Jan 2026, Shift 2
Correct answer: (2) 40 โ 8(4m + 6w) = 10(3m + 7w) โ 2m = 22w โ m = 11w. Work = 8 ร 50w = 400 โ 10 women: 40 days.
Q26. The percentage profit earned by selling an article for โน1920 is equal to the percentage loss incurred by selling the same article for โน1280. At what price should the article be sold to earn a 25% profit? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (1) โน2000 โ CP = (1920 + 1280)/2 = 1600 โ ร 1.25 = 2000. (The Hindi version had a "1920" typo in both places; the English version has 1280.)
Q27. A man has โน480 in notes of one rupee, five rupees and ten rupees. The number of notes of each denomination is equal. How many notes does he have in total? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (4) 90 โ n notes of each type: 16n = 480 โ n = 30 โ total 90.
Q28. In a class, free notebooks were distributed equally among the students. The number of notebooks each student got was one-eighth of the total number of students. If the number of students had been half, each student would have got 16 notebooks. How many notebooks were distributed in total? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (3) 512 โ n students, n/8 each โ total nยฒ/8 = (n/2) ร 16 = 8n โ n = 64 โ total 512.
Q29. Machine P can print one lakh books in 8 hours, machine Q can print the same books in 10 hours, while machine R can print them in 12 hours. All the machines are started at 9 am, but machine P is switched off at 11 and the remaining two machines complete the work. At approximately what time will the work of printing one lakh books be completed? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 1
Correct answer: (4) About 1:00 PM โ LCM 120: P 15, Q 12, R 10 units/h. In 2 hours 74 units; the remaining 46 รท 22 โ 2.09 hours โ about 1:05 PM โ 1 o'clock.
Q30. The price of sugar increases by 25%. By what percent should a family reduce its consumption to keep its expenditure the same? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (2) 20% โ 25/125 ร 100.
Q31. The price of 2 sarees and 4 shirts is โน1600. With the same money, 1 saree and 6 shirts can be bought. If someone wants to buy 12 shirts, how many rupees will he have to pay? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (2) โน2400 โ 2S + 4H = 2S + 12H (second multiplied by 2 = 3200) โ 8H = 1600 โ H = 200 โ 12 ร 200 = 2400.
Q32. Ruban has calculated that if he travels at a speed of 10 km/h, he will reach point A at 2 pm. If he travels at a speed of 15 km/h, he will reach there at 12 noon. At what speed should he travel to reach point A at 1 pm? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (3) 12 km/h โ d/10 โ d/15 = 2 โ d = 60; at 10 km/h 6 hours โ start 8 AM; up to 1 PM = 5 hours โ 60/5 = 12.
Q33. A and B can complete a job in 15 days and 10 days respectively. They started working together, but after 2 days B had to leave and A completed the remaining work alone. In how many days was the whole work completed? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (3) 12 days โ in 2 days 2 ร 1/6 = 1/3; the remaining 2/3 by A alone = 10 days โ total 12.
Q34. When a plot is sold for โน18,700, the owner incurs a loss of 15%. At what price must the plot be sold to get a profit of 15%? MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 2
Correct answer: (3) โน25,300 โ CP = 18700/0.85 = 22000 โ ร 1.15 = 25300.
Q35. A farmer covered a distance of 61 kilometres in 9 hours. He covered some distance on foot at a speed of 4 km/h and the rest on a bicycle at a speed of 9 km/h. What is the distance covered on foot? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (3) 16 km โ x/4 + (61 โ x)/9 = 9 โ 9x + 244 โ 4x = 324 โ x = 16.
Q36. The ratio of the speeds of a : b : c is 8 : 7 : 6. Find the ratio of the times taken by them. MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (1) 21:24:28 โ 1/8 : 1/7 : 1/6, ร 168 = 21 : 24 : 28.
Q37. Mohak sold an article for โน4,510 and incurred a loss of 45% on it. At what price should he have sold the article to get a profit of 45%? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (3) โน11,890 โ CP = 4510/0.55 = 8200 โ ร 1.45 = 11890.
Q38. The ratio of the speeds of two trains is 7 : 8. If the second train covers a distance of 400 kilometres in 4 hours, what will be the speed of the first train? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (4) 87.5 โ second = 100 โ first = 100 ร 7/8 = 87.5.
Q39. If 6 men and 8 boys can do a job in 10 days, while 26 men and 48 boys can do the same job in 2 days, in how many days will 15 men and 20 boys do the same kind of job? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 2
Correct answer: (1) 4 days โ 10(6m + 8b) = 2(26m + 48b) โ 8m = 16b โ m = 2b. Work = 10 ร 20b = 200; 15m + 20b = 50b โ 4 days.
Source of all Q1โQ39: MPESB SI Prelims 2025, Rationality section (date and shift given on each question).
๐ 10. Syllogism (10 min read)
How to draw it with Venn diagrams
"Some A are not B" = at least one part of A lies outside B
Definite Rules
| Statement | Definitely true | Not definite (only a possibility) |
|---|---|---|
| All A are B | Some A are B ยท Some B are A | All B are A |
| Some A are B | Some B are A | All A are B ยท All B are A |
| No A is B | No B is A ยท Some A are not B ยท Some B are not A | โ |
| Some A are not B | (it has no conversion) | โ |
Shortcut for combining two Statements (remove the common middle term)
| Statement 1 (AโB) | Statement 2 (BโC) | Conclusion (AโC) |
|---|---|---|
| All | All | All A are C |
| All | No | No A is C |
| Some | All | Some A are C |
| Some | No | Some A are not C |
| All | Some | No definite conclusion |
| Some | Some | No definite conclusion |
| No | All | Some C are not A (not about A, about C) |
โข If both statements are positive, no negative conclusion is definite.
โข A possibility conclusion is true when it does not break any definite fact.
โข Either-or: when neither of two conclusions is definite, but they form a "some" + "no" pair (or "all" + "some not") on the same subject-predicate โ "Either I or II".
โข Don't apply real-world knowledge โ if "All dogs fly" is given, accept exactly that.
โข A possibility conclusion is true when it does not break any definite fact.
โข Either-or: when neither of two conclusions is definite, but they form a "some" + "no" pair (or "all" + "some not") on the same subject-predicate โ "Either I or II".
โข Don't apply real-world knowledge โ if "All dogs fly" is given, accept exactly that.
Solved Example 1: Statements: All dogs are animals. All animals are loyal. Conclusions: I. All dogs are loyal. II. Some loyal ones are animals.
Dogs โ animals โ loyal. I โ (all + all = all). II โ (all animals are loyal โ some loyal ones are animals). โ Both.
Solved Example 2: Statements: Some pens are books. No book is a notebook. Conclusions: I. Some pens are not notebooks. II. Some notebooks are pens.
Some + no = some pens are not notebooks โ I โ. II is only possible, not definite โ โ. โ Only I.
Solved Example 3 (possibility): Statements: All cats are dogs. No dog is a rat. Conclusions: I. No cat is a rat. II. There is a possibility that some rats are cats.
All + no = no cat is a rat โ I โ. II clashes with this โ โ. โ Only I.
โ ๏ธ Exam Traps:
- "All A are B" does not give "All B are A".
- "Some" means "at least one" โ it can also be "all".
- If the subject of the conclusion is reversed, check it only after applying the conversion rule.
โ๏ธ Practice MCQs (self-made โ not PYQs) ยท Options: (1) Only I (2) Only II (3) Either I or II (4) Both (5) Neither
P1. All pens are books. Some books are notebooks. I. Some pens are notebooks. II. Some notebooks are books. Practice MCQ
Answer: (2) Only II โ all + some = nothing definite (I โ); conversion of "some books are notebooks" (II โ).
P2. No cat is a dog. All dogs are animals. I. Some animals are not cats. II. No cat is an animal. Practice MCQ
Answer: (1) Only I โ no + all = some animals (those that are dogs) are not cats. II is not definite.
P3. All roses are flowers. All flowers are plants. I. All roses are plants. II. All plants are roses. Practice MCQ
Answer: (1) Only I
P4. Some boys are girls. No girl is tall. I. Some boys are not tall. II. There is a possibility that all boys are tall. Practice MCQ
Answer: (1) Only I โ the boys who are girls are not tall โ II is impossible.
P5. Some A are B. Some B are C. I. Some A are C. II. No A is C. Practice MCQ
Answer: (3) Either I or II โ neither is definite, but they are a complementary "some" + "no" pair.
๐ 11. Statement-Conclusion, Statement-Assumption & Cause-Effect (Statement-based Reasoning) (7 min read)
| Type | What is asked | Rule for accepting it |
|---|---|---|
| Conclusion | What definitely follows from the statement | It must come directly from the facts of the statement only; not your own opinion/outside information. Extreme conclusions with "only", "always", "all" are often โ. |
| Assumption | What the speaker has already taken for granted (not written) | If, without that belief, the statement would become meaningless โ then it is an assumption โ. (Negation test) |
| Course of Action | What step should be taken | Practical + reduces the problem + not extreme (Topic 8). |
| Argument (Strong/Weak) | Whether the argument is strong or weak | Linked to the main issue, fact-based = strong; emotional/vague/mere example = weak. |
| CauseโEffect | Of two events, which is the cause and which the effect | What happened first and what caused the second; both can also be effects of some third cause, or independent. |
Example (Assumption): Statement: "The government raised the fine for riding without a helmet to โน1000." Assumptions: I. People will wear helmets because of the higher fine. II. Earlier everyone used to wear helmets.
Without I, there is no point in raising the fine โ โ. II is the opposite (if everyone wore them, why would the rule be needed) โ โ. โ Only I.
Example (Conclusion): Statement: "Only graduates can apply for this post. Ramesh has applied." I. Ramesh is a graduate. II. Ramesh will get the job.
I โ (he applied as per the rule). II has no basis in the statement โ. โ Only I.
Example (Cause-Effect): (A) The city had heavy rain for 3 days in a row. (B) Many low-lying localities of the city were waterlogged.
Rain โ waterlogging: A is the cause, B is its effect.
โ ๏ธ Exam Traps:
- Even a conclusion that seems true is โ if it does not follow from the statement.
- In cause-effect, the order of time alone is not enough โ a direct link is needed.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Statement: "Send your children to XYZ School โ 95% of its students pass in first division every year." (advertisement). Assumptions: I. Parents want a school with good results. II. No one gets a first division in other schools. Practice MCQ
Answer: (1) Only I โ II is extreme.
P2. (A) The wheat crop was very poor this year. (B) The price of flour rose in the market. Practice MCQ
Answer: (1) โ low supply โ prices rose.
P3. Argument: "Should mobile phones be banned in school?" I. Yes, they distract attention in class. II. No, all big countries use mobiles. Practice MCQ
Answer: (1) โ I is directly linked to the issue; II is irrelevant.
๐ 12. Venn Diagrams (6 min read)
Identifying which figure best shows the relationship between three (or two) classes.
| Words | Relationship | Figure |
|---|---|---|
| Rupee, currency, money | One inside another (rupee โ currency โ money) | (a) |
| Man, woman, human | Man and woman separate, both inside human | (b) |
| Teacher, woman, mother | Mother โ woman; teacher overlaps both | (c) |
| Doctor, lawyer, man | Doctor and lawyer separate; both overlap with man (some doctors are men) | Two separate circles, both cutting a third |
| Bird, crow, cow | Crow โ bird; cow separate | One inside another + one separate |
Venn with numbers (two sets)
n(A โช B) = n(A) + n(B) โ n(A โฉ B) ยท None at all = total โ n(A โช B)
Solved Example: Of 50 students, 30 like Hindi, 25 like English, 10 like both. How many like neither?
30 + 25 โ 10 = 45 โ neither = 50 โ 45 = 5. Only Hindi = 30 โ 10 = 20; only English = 15.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Which figure best shows "Bhopal, Madhya Pradesh, India"? Practice MCQ
Answer: (2)
P2. "Hand, finger, nail" โ relationship? Practice MCQ
Answer: (1) โ nail โ finger โ hand (part relationship).
P3. Of 60 people, 35 drink tea, 30 drink coffee, 8 drink neither. How many drink both? Practice MCQ
Answer: (2) 13 โ at least one = 52 โ 35 + 30 โ x = 52 โ x = 13.
๐ 13. Analogy (6 min read)
A : B :: C : ? โ the relationship in the first pair is the same in the second pair. First say the relationship in a short sentence ("a doctor works in a hospital"), then apply the same sentence to C.
| Type of relationship | Example |
|---|---|
| Place of work | Doctor : Hospital :: Teacher : School |
| Tool : work | Pen : Write :: Knife : Cut |
| Creature : home | Bird : Nest :: Lion : Den ยท Bee : Hive |
| Young one | Cow : Calf :: Dog : Puppy |
| Measuring instrument | Temperature : Thermometer :: Earthquake : Seismograph |
| Antonym / synonym | Hot : Cold :: High : Low |
| Country : capital / state : capital | India : New Delhi :: Madhya Pradesh : Bhopal |
| Number (square, cube, nยฒ ยฑ 1) | 3 : 27 :: 5 : 125 (cube) ยท 6 : 35 :: 8 : 63 (nยฒ โ 1) |
| Letters (shift) | ACE : BDF :: GIK : HJL (+1) |
Solved Example: 7 : 50 :: 9 : ?
7ยฒ + 1 = 50 โ 9ยฒ + 1 = 82.Solved Example: CAT : DBU :: DOG : ?
Every letter +1 โ EPH.โ ๏ธ Trap: In number analogy more than one pattern may fit โ take the pattern that gives only one answer among the options. Keep the direction (A โ B); don't apply it in reverse (B โ A).
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Doctor : Hospital :: Teacher : ? Practice MCQ
Answer: (2) School
P2. 3 : 27 :: 5 : ? Practice MCQ
Answer: (3) 125
P3. 6 : 35 :: 8 : ? Practice MCQ
Answer: (1) 63 โ nยฒ โ 1.
P4. Bird : Nest :: Lion : ? Practice MCQ
Answer: (2) Den
P5. ACE : BDF :: GIK : ? Practice MCQ
Answer: (1) HJL
๐ 14. Classification โ Odd One Out (5 min read ยท 2 PYQs)
Three of the four share some common property; the one that is different is the answer. Check-list: category (fruit/vegetable, planet/satellite), prime/composite, even/odd, square/cube, divisibility by some number, gap between letters, vowel/consonant.
Solved Example: 27, 64, 125, 144
27 = 3ยณ, 64 = 4ยณ, 125 = 5ยณ; 144 = 12ยฒ (not a cube) โ 144.Solved Example: ACE, BDF, GIK, MNO
The first three have a +2 gap; MNO has +1 โ MNO.โ ๏ธ Trap: If two different properties give two different answers (e.g. in 11, 22, 33, 44 "even/odd" splits them two and two), find a property that separates only one.
๐ฏ Official PYQs โ MPESB SI Prelims 2025 (Analytical Ability section)
Q1. Which word is not a type of tax? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Analytical Ability)
Correct answer: (4) Subsidy โ a subsidy is help given by the government, not a tax.
Q2. Find the two-digit number that is not divisible by 4? MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Analytical Ability)
Correct answer: (4) 94 โ 94 รท 4 = 23.5; the other three are divisible by 4.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. 17, 23, 29, 33 Practice MCQ
Answer: (4) 33 โ the rest are prime; 33 = 3 ร 11.
P2. Mercury, Venus, Moon, Mars Practice MCQ
Answer: (3) Moon โ a satellite; the rest are planets.
P3. Rose, Lotus, Jasmine, Mango Practice MCQ
Answer: (4) Mango โ a fruit; the rest are flowers.
๐ 15. Series (Number, Letter & Alphanumeric Series) (8 min read)
Number Series โ Order of checking
- Find the difference โ constant (AP)? increasing? difference of differences?
- Multiplication/division (ร2, ร3) or ร k + m (ร2 + 1).
- Near squares/cubes: nยฒ, nยฒ ยฑ 1, nยณ, nยณ ยฑ 1, n(n + 1).
- Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37... (1 is not prime).
- Alternate: 1st, 3rd, 5th form one series; 2nd, 4th, 6th another.
| Pattern | Series | Next |
|---|---|---|
| Differences 2, 4, 6, 8... | 4, 6, 10, 16, 24 | 34 |
| n(n + 1) | 2, 6, 12, 20, 30 | 42 |
| nยฒ + 1 | 2, 5, 10, 17, 26 | 37 |
| nยณ โ 1 | 0, 7, 26, 63, 124 | 215 |
| ร2 + 1 | 3, 7, 15, 31, 63 | 127 |
| ร2 + 1, ร2 + 2, ร2 + 3... | 3, 7, 16, 35, 74 | 153 |
| Squares of prime numbers | 4, 9, 25, 49, 121 | 169 |
Letter / Alphanumeric Series
Convert letters into numbers (A = 1...) and apply the same number rules. If there are groups, look at the first letter, second letter of each group separately.
Solved Example 1: 4, 9, 25, 49, 121, ?
2ยฒ, 3ยฒ, 5ยฒ, 7ยฒ, 11ยฒ โ squares of prime numbers โ 13ยฒ = 169 (12ยฒ = 144 is the trap).Solved Example 2: BDF, HJL, NPR, ?
B2 D4 F6 H8 J10 L12 N14 P16 R18 โ next T20 V22 X24 โ TVX.Solved Example 3 (letter repeat): a a b _ a a b b a _ b b
Pattern "aabb" repeated โ blanks: b, a.โ ๏ธ Traps:
- In "wrong term" questions, first confirm the pattern, then pick the term that does not match it.
- In letter series, after Z comes A again (wrap).
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. 5, 11, 23, 47, ? Practice MCQ
Answer: (2) 95 โ ร2 + 1.
P2. 1, 8, 27, 64, ?, 216 Practice MCQ
Answer: (3) 125
P3. A, C, F, J, O, ? Practice MCQ
Answer: (2) U โ +2, +3, +4, +5, +6 โ 15 + 6 = 21.
P4. B2, D4, F6, H8, ? Practice MCQ
Answer: (2) J10
P5. 7, 10, 8, 11, 9, 12, ? Practice MCQ
Answer: (1) 10 โ +3, โ2 alternately (or: 7, 8, 9, 10 and 10, 11, 12 alternate).
P6. AZ, BY, CX, ? Practice MCQ
Answer: (2) DW โ opposite letter pairs.
๐ 16. Missing Number (Matrix/Figure) (5 min read)
Look for the pattern in rows; if not found, in columns. Common patterns: sum, product, aยฒ + bยฒ, (a + b) ร 2, a ร b โ c, middle number = sum/product of the rest.
Solved Example 1:
3 4 25
5 12 169
6 8 ?
Row pattern: aยฒ + bยฒ โ 9 + 16 = 25 โ, 25 + 144 = 169 โ โ 36 + 64 = 100.
Solved Example 2 (column):
3 4 7
5 6 2
16 20 ?
Third row = (first + second) ร 2: (3 + 5) ร 2 = 16 โ, (4 + 6) ร 2 = 20 โ โ (7 + 2) ร 2 = 18.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Rows: (2, 3, 4 โ 24), (3, 4, 5 โ 60), (4, 5, 6 โ ?) Practice MCQ
Answer: (3) 120 โ product of all three.
P2. Rows: (5, 3 โ 34), (6, 2 โ 40), (7, 4 โ ?) Practice MCQ
Answer: (2) 65 โ aยฒ + bยฒ: 25 + 9 = 34, 36 + 4 = 40, 49 + 16 = 65.
๐ 17. Mathematical Operations, Symbol Substitution & Inequality (6 min read)
Symbol Substitution โ Method
- First replace the given symbols with the real symbols and rewrite the whole expression.
- Then BODMAS: brackets โ division (รท) โ multiplication (ร) โ addition (+) โ subtraction (โ). (Division and multiplication in left-to-right order.)
Solved Example: '+' means 'ร', 'โ' means 'รท', 'ร' means 'โ', 'รท' means '+'. 8 + 3 โ 4 ร 2 รท 5 = ?
After replacing: 8 ร 3 รท 4 โ 2 + 5 = 24 รท 4 โ 2 + 5 = 6 โ 2 + 5 = 9.
Solved Example (interchange): Interchanging which two signs will make the equation correct? 8 ร 3 + 4 โ 2 = 18
Interchange + and ร: 8 + 3 ร 4 โ 2 = 8 + 12 โ 2 = 18 โ
Inequality โ Rules
- A > B โฅ C = D โ comparing A and D: if there is no opposite sign (< or โค) on the way, they connect โ A > D.
- If two signs point in opposite directions (> and <) โ no definite relation.
- If even one sign in the chain is strict (>), the result is strict (>); if all are โฅ/=, then โฅ.
- "Either A โฅ B or A < B" type โ when neither is definite and together they cover all possibilities.
Solved Example: A > B โฅ C = D < E. Conclusions: I. A > D II. E > B
I: A > B โฅ C = D โ โ. II: B โฅ C = D < E โ direction changed โ not definite โ. โ Only I.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. If P = +, Q = โ, R = ร, S = รท, then 20 S 4 R 3 P 6 Q 2 = ? Practice MCQ
Answer: (2) 19 โ 20 รท 4 ร 3 + 6 โ 2 = 15 + 6 โ 2 = 19.
P2. Which signs should be interchanged to make 8 ร 3 + 4 โ 2 = 18 correct? Practice MCQ
Answer: (1) โ with (2): 8 ร 3 โ 4 + 2 = 22; with (3): 8 โ 3 + 4 ร 2 = 13.
P3. Statement: M โฅ N > O, O = P, P โค Q. Conclusions: I. M > P II. Q โฅ O Practice MCQ
Answer: (3) Both โ M โฅ N > O = P โ M > P โ; Q โฅ P = O โ Q โฅ O โ.
๐ 18. Seating Arrangement โ Linear & Circular (8 min read)
Left-Right Rules
| Situation | Right | Left |
|---|---|---|
| Row, facing North (you are also looking the same way) | Your right | Your left |
| Row, facing South (towards you) | Your left | Your right |
| Round table, facing the centre | Anticlockwise | Clockwise |
| Round table, facing outward | Clockwise | Anticlockwise |
Method: (1) First fill in the definite information (e.g. "C is in the middle", "P is opposite S"). (2) Then the pair information (immediate right/left). (3) Eliminate cases using the "not" information. (4) Draw each case in a separate diagram.
Solved Example 1 (Linear): A, B, C, D, E are sitting in a row facing North. C is in the middle. A is to the immediate right of C. D is to the immediate left of C. B is at one of the ends. E is not at the right end.
Positions 1 (left end) โ 5 (right end): C = 3, A = 4, D = 2. B and E remain: 1 and 5. E is not at the right end (5) โ E = 1, B = 5.
Left โ E D C A B โ Right (all facing North)
Between D and A = C; at the left end = E.
Solved Example 2 (Circular): P, Q, R, S, T, U at a round table facing the centre. S is directly opposite P. Q is to the immediate left of P. T is to the immediate right of S. U is not a neighbour of P.
Put P at the top. Q = P's left = the next seat clockwise. S at the bottom (opposite). T = S's right = the next seat anticlockwise. The two remaining seats are on the left side, going down from P; U is not next to P โ U lower-left, R upper-left.
P
R Q
U T
S
(clockwise, seen from above: P โ Q โ T โ S โ U โ R)
Opposite Q = U; to the immediate right of P = R.
โ ๏ธ Traps:
- "Immediate right" โ "right (anywhere on the right side)".
- At a round table, the right of a person facing "the centre" = anticlockwise โ this is where most mistakes happen.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. P, Q, R, S, T are in a row facing North. P is at the left end. R is to the immediate right of T. S is to the immediate left of Q. Q is not at the right end. Who is in the middle? Practice MCQ
Answer: (2) Q โ Order: P S Q T R. (In the other case, P T R S Q, Q would be at the right end, so it is rejected.)
P2. A, B, C, D, E, F are sitting at a round table facing the centre. D is directly opposite A. B is to the immediate right of A. E is to the immediate left of D. C is directly opposite B. Who is directly opposite F? Practice MCQ
Answer: (3) E โ Clockwise seats 0โ5: A = 0, D = 3, B = 5 (A's right = anticlockwise), E = 4 (D's left = clockwise), C = 2 (opposite B), F = 1 โ opposite F is seat 4 = E.
๐ 19. Puzzles โ Floor, Table & Number Puzzles (8 min read ยท 3 PYQs)
Floor Puzzle Method
Write the floors from 1 (lowest/ground) upwards. "Immediately above/below" = consecutive floors; "x people in between" = floor difference x + 1. Definite information first, then pairs, then cases.
Solved Example (Floor): A, B, C, D, E live on different floors of a 5-storey building (1 = lowest). B lives at the top. A is immediately below B. D is immediately above E. C is not on floor 1.
B = 5, A = 4. In the remaining 1, 2, 3, (E, D) are consecutive: (E1, D2) or (E2, D3). In the second case C = 1 โ rejected. โด E = 1, D = 2, C = 3.
5 B
4 A
3 C
2 D
1 E
Table (Grid) Method โ "who likes what"
Solved Example: Aman, Bablu, Chetan and Deepak like different colours (red, blue, green, yellow). Aman does not like red or blue. Bablu likes green. Chetan does not like blue. Which colour does Deepak like?
Bablu = green. Aman: red โ blue โ green (taken) โ yellow. Chetan: blue โ โ red. Deepak = blue.
Number Puzzles โ Tricks
- Remainder 1 less than every divisor (9 by 10, 8 by 9 ... 1 by 2): number = LCM โ 1.
- Heads-legs: assume all are 2-legged โ extra legs รท 2 = number of 4-legged ones.
- Spare tyre: total tyre-distance รท tyres running at the same time.
๐ฏ Official PYQs โ MPESB SI Prelims 2025 (Rationality section)
Q1. When a number is divided by 10 the remainder is 9, when divided by 9 the remainder is 8, and so on, when divided by 2 the remainder is 1. What is the smallest such positive number? MPESB SI Prelims 2025 โ 19 Jan 2026, Shift 2
Correct answer: (3) 2519 โ LCM(2, 3, ..., 10) = 2520 โ 2520 โ 1 = 2519.
Q2. A car has 4 tyres and 1 extra (spare) tyre. Each tyre can run a maximum of 20,000 miles, after which it wears out. What is the maximum distance the car can travel before you are forced to buy a new tyre? You are allowed to change tyres (use the spare tyre) an unlimited number of times. MPESB SI Prelims 2025 โ 20 Jan 2026, Shift 1
Correct answer: (2) 25000 โ total capacity 5 ร 20000 = 100000 tyre-miles; 4 tyres at a time โ 100000/4 = 25000 miles.
Q3. A person has some hens and cows. If the number of heads is 48 and the number of legs is 140, what will be the number of hens? MPESB SI Prelims 2025 โ 21 Jan 2026, Shift 1
Correct answer: (4) 26 โ assume all have 2 legs: 96; extra 44 รท 2 = 22 cows โ hens 48 โ 22 = 26.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. In the Floor example above, who lives on floor 3? Practice MCQ
Answer: (2) C
P2. A farm has some ducks and goats. There are 30 heads and 84 legs. How many goats? Practice MCQ
Answer: (2) 12 โ 84 โ 60 = 24 รท 2 = 12.
๐ 20. Data Sufficiency (5 min read ยท 1 PYQ)
You do not have to find the answer, only decide whether the given information is enough or not. Check I alone first, then II alone, then both together.
| Option (usual order) | When |
|---|---|
| Only I is sufficient | I gives a definite answer, II does not |
| Only II is sufficient | II gives a definite answer, I does not |
| Either I or II | Either one alone is enough |
| I and II together | Neither alone, but together enough |
| Neither I nor II | Not enough even together |
๐ฏ Official PYQ โ MPESB SI Prelims 2025 (Analytical Ability section)
Q1. Question: How many children does M have? Statements: I. H is the only daughter of X, and X is M's wife. II. K and J are M's brothers. MPESB SI Prelims 2025 โ 16 Jan 2026, Shift 1 (Analytical Ability)
Correct answer: (4) โ I only tells us that there is one daughter; how many sons there are is not known. II gives M's brothers, not children. Even together, the count is not obtained.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. What day was 10 March? I. 8 March was a Monday. II. 12 March was a Friday. Practice MCQ
Answer: (3) โ From I: 10 March = Wednesday; from II also: 12 (Friday) โ 2 = Wednesday.
P2. How is A related to B? I. A is C's brother. II. C is B's daughter. Practice MCQ
Answer: (4) โ Together: A is B's son.
๐ 21. Input-Output (Machine Input) โ Basics (4 min read)
An input line changes by some rule at every step. Compare the steps carefully to identify the rule โ often: bringing the largest/smallest number or the first word in dictionary order to the left (or right) end one by one.
Solved Example (words, dictionary order from the left):
Input : tiger apple moon ball
Step I: apple tiger moon ball
Step II: apple ball tiger moon
Step III: apple ball moon tiger โ final (3 steps)
In every step, the first word in dictionary order among the remaining words comes forward.
Solved Example (numbers, largest to the left):
Input : 25 12 47 8 33
Step I: 47 25 12 8 33
Step II: 47 33 25 12 8 โ final (2 steps)
โ ๏ธ Trap: The relative order of the other elements stays the same in every step (unless the rule says otherwise) โ this is how wrong options get eliminated.
โ๏ธ Practice MCQ (self-made โ not PYQs)
P1. Using the word rule above, what will be Step II for the Input "sun cat egg ant"? Practice MCQ
Answer: (1) โ Step I: ant sun cat egg; Step II: ant cat sun egg.
๐ 22. Dice & Cube (8 min read)
Dice Rules
- Standard dice: sum of opposite faces is 7 โ (1, 6), (2, 5), (3, 4).
- Faces seen in the same view are adjacent to each other, never opposite.
- One face common (in two views): starting from the common face, write the faces of both views clockwise; faces that come in the same position are opposite to each other.
- Two faces common: the remaining third faces are opposite to each other.
- If the four neighbours of a face are known โ the remaining sixth face is its opposite.
Open dice (Net) โ opposite faces
[1]
[2] [3] [4] [5]
[6]
โข In the straight row, faces with one face between them are opposite: 2โ4, 3โ5
โข The top and bottom faces are opposite: 1โ6
Solved Example 1 (one common): Two positions of a dice โ in the first the faces clockwise are (3, 5, 1) and in the second (3, 2, 4). Opposite of 5?
From the common 3: 3 โ 5 โ 1 and 3 โ 2 โ 4. In the same position: 5 โ 2, 1 โ 4 โ opposite of 5 is 2. (The remaining 3 and 6 are also opposite.)
Solved Example 2 (two common): Two views: (2, 3, 5) and (2, 3, 6).
2 and 3 are common โ the remaining 5 and 6 are opposite.Painted Cube (cut into n ร n ร n, all outer faces painted)
| Type | Formula | n = 3 | n = 4 |
|---|---|---|---|
| Total small cubes | nยณ | 27 | 64 |
| 3 faces painted (corners) | 8 (always) | 8 | 8 |
| 2 faces painted (edges) | 12(n โ 2) | 12 | 24 |
| 1 face painted | 6(n โ 2)ยฒ | 6 | 24 |
| No face painted (inside) | (n โ 2)ยณ | 1 | 8 |
Minimum cuts to get nยณ pieces = 3(n โ 1) (e.g. 6 cuts for 27 pieces).
โ ๏ธ Traps: Not every dice is "standard" โ unless stated, do not apply the rule of 7; work it out from the views only. Check: never make two faces seen in the same view opposite.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. Two positions (clockwise): (4, 1, 5) and (4, 2, 6). Opposite of 5? Practice MCQ
Answer: (3) 6 โ 1 โ 2, 5 โ 6, the remaining 4 โ 3.
P2. A 5 ร 5 ร 5 painted cube is cut into 125 small cubes. How many cubes will have exactly two faces painted? Practice MCQ
Answer: (2) 36 โ 12 ร 3. (1 face = 54, none = 27, 3 faces = 8; total 125 โ)
P3. In four views, the neighbours of 1 are seen to be 2, 3, 4, 5. Opposite of 1? Practice MCQ
Answer: (3) 6
๐ 23. Mirror & Water Image (7 min read)
| Mirror image (vertical mirror) | Water image (water surface) | |
|---|---|---|
| What gets reversed | Left โ right (lateral inversion) | Top โ bottom |
| Order of the letters of a word | Gets reversed + every letter flips | Order stays the same, every letter flips upside down |
| Example: POLICE | POLICE | POLICE |
| Capital letters that do not change | A H I M O T U V W X Y | B C D E H I K O X |
Mirror image of a clock: subtract the given time from 11:60 (for times between 11:00 and 12:59, from 23:60).
โข 4:20 โ 11:60 โ 4:20 = 7:40 ยท 3:15 โ 8:45 ยท 12:35 โ 23:60 โ 12:35 = 11:25
Water image of a clock (exam shortcut): subtract the given time from 18:30 (if the minutes are more than 30, from 17:90). This is the rule given in exam books.
โข 4:20 โ 11:60 โ 4:20 = 7:40 ยท 3:15 โ 8:45 ยท 12:35 โ 23:60 โ 12:35 = 11:25
Water image of a clock (exam shortcut): subtract the given time from 18:30 (if the minutes are more than 30, from 17:90). This is the rule given in exam books.
Solved Example: Which word will look exactly the same in a vertical mirror โ MOM, DAD, NOON, BOB?
The word must be a palindrome and every letter must be mirror-symmetric. D, N, B are not symmetric โ MOM.
Solved Example: Which word will look the same in water โ BOX, BAT, CAR, TOY?
In a water image the order does not change; every letter must be top-bottom symmetric: B, O, X โ โ BOX.
โ ๏ธ Traps:
- In a mirror image, flipping only the letters is not enough โ the order is also reversed (right โ left).
- In a mirror question, see on which side the mirror is placed (right/below) โ a mirror placed below = like a water image.
- Official figure questions come with image options; there, move every part to the opposite side at an equal distance from the mirror line.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. The mirror image of 3:15 on a clock will look like which time? Practice MCQ
Answer: (2) 8:45
P2. Mirror image of 12:35 on a clock? Practice MCQ
Answer: (1) 11:25 โ 23:60 โ 12:35.
P3. Which of these letters will look changed in a mirror? Practice MCQ
Answer: (3) R โ the rest are vertically symmetric.
๐ 24. Paper Folding / Cutting (5 min read)
โข On opening, every hole/cut is repeated on the other side of the fold line at an equal distance (like a mirror).
โข Number of holes = holes punched ร 2number of folds (if the hole goes through all layers and is not on the fold line). 1 fold โ ร2, 2 folds โ ร4, 3 folds โ ร8.
โข A half cut made on the fold line (e.g. a semicircle) becomes one full shape (a full circle) on opening.
โข Order of opening = reverse of the order of folding (open the last fold first).
โข Number of holes = holes punched ร 2number of folds (if the hole goes through all layers and is not on the fold line). 1 fold โ ร2, 2 folds โ ร4, 3 folds โ ร8.
โข A half cut made on the fold line (e.g. a semicircle) becomes one full shape (a full circle) on opening.
โข Order of opening = reverse of the order of folding (open the last fold first).
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. A square paper is folded in half, then in half again, and 1 hole is punched through all layers (away from the fold line). How many holes on opening? Practice MCQ
Answer: (3) 4
P2. Paper folded three times, 1 hole through all layers. On opening? Practice MCQ
Answer: (2) 8 โ 2ยณ.
P3. A paper is folded once and a semicircle is cut on the fold line. What will be seen on opening? Practice MCQ
Answer: (2)
๐ 25. Embedded Figures & Counting Figures (7 min read)
Embedded Figure โ Method
- Identify some special part of the given small figure (a sharp corner, a slanting line, a curve).
- Look for the same part in the larger figures (options) in the same size and the same direction โ usually rotating is not allowed.
- Then match the remaining lines; if even one line is missing, the option is โ.
Counting Figures โ Formulas
| Figure | Formula | Example |
|---|---|---|
| Triangle with lines from the vertex to the base, base in n parts | n(n + 1)/2 | n = 3 โ 6; n = 4 โ 10 |
| The above figure + lines parallel to the base (total m including the base) | m ร n(n + 1)/2 | n = 3, m = 2 โ 12 |
| Square + both diagonals | 8 triangles | โ |
| Squares in an n ร n grid | 1ยฒ + 2ยฒ + ... + nยฒ | 3ร3 โ 14; 4ร4 โ 30 |
| Rectangles in an m ร n grid (including squares) | [m(m + 1)/2] ร [n(n + 1)/2] | 2ร2 โ 3 ร 3 = 9; 2ร3 โ 3 ร 6 = 18 |
โ ๏ธ Trap: If the formula does not fit, use the labelling method: write letters (A, B, C...) at every corner/intersection point and count in order from small to large (1-part figures, 2-part figures...) โ keep writing them down to avoid repetition.
โ๏ธ Practice MCQs (self-made โ not PYQs)
P1. In a triangle, 3 lines are drawn from the vertex to the base (base divided into 4 parts). Total triangles? Practice MCQ
Answer: (2) 10 โ 4 ร 5/2.
P2. How many squares in total in a 4 ร 4 chessboard-like grid? Practice MCQ
Answer: (3) 30 โ 16 + 9 + 4 + 1.
P3. Total rectangles (including squares) in a 2 ร 2 grid? Practice MCQ
Answer: (3) 9 โ 3 ร 3.
โ Last-week Revision Checklist
- Blood relation: "only son/daughter" = oneself; family tree + gender.
- Ranking: L + R โ 1; interchange = the other person's old position; "other than" โ โ2.
- Direction: (x, y) method; morning shadow West, evening East; North face โ right is East.
- Clock: |30H โ 5.5M|; hour hand 0.5ยฐ/min; meeting M = 60H/11; gain/loss ratio.
- Calendar: year +1 (+2 if 29 Feb is in between); 1800/1900 not leap; 53 days โ 1/7 or 2/7.
- Coding: check the pattern on the whole word; opposite letters sum to 27.
- Dictionary: letter by letter; the shorter prefix word comes first.
- Decision: safe + legal + direct + consult; extreme/ignore โ.
- Arithmetic: profit-loss, time-speed, work โ 3โ4 questions in every shift of Rationality.