📑 Topics on this page (Jump to Topic):
📌 1. Basic Rules
- Tank capacity = LCM of the times; a filling pipe does positive (+) work and an emptying pipe negative (−) work.
- A fills in a hours, B empties in b hours (b > a) → together the tank fills in ab/(b − a).
- If a leak makes filling take t hours longer: leak alone empties in a(a + t)/t.
✏️ Example: A fills in 10 h, B in 15 h. LCM 30 → 3 + 2 = 5/hour → 6 hours.
⚠️ Exam Traps:
- If the emptying pipe is faster (b < a), a full tank will empty — watch the signs.
📌 2. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. Two pipes A and B can fill a tank in 4 and 8 hours. If both are opened together, how long will the tank take to fill? Practice
Correct answer: (B)
Solution: Time = ab/(a + b) = 4×8/12 = 2.67 hours.
Solution: Time = ab/(a + b) = 4×8/12 = 2.67 hours.
Q2. Pipe A fills a tank in 4 hours and pipe B empties it in 8 hours. If both are opened, in how much time will the empty tank fill? Practice
Correct answer: (C)
Solution: Net rate = 1/4 − 1/8 → time = ab/(b − a) = 32/4 = 8 hours.
Solution: Net rate = 1/4 − 1/8 → time = ab/(b − a) = 32/4 = 8 hours.
Q3. A pipe fills a tank in 10 hours, but due to a leak it takes 11 hours. In how much time will the leak alone empty the full tank? Practice
Correct answer: (D)
Solution: Leak = a(a + t)/t = 10×11/1 = 110 hours.
Solution: Leak = a(a + t)/t = 10×11/1 = 110 hours.
Q4. Pipes A and B fill a tank in 8 and 15 hours, while pipe C empties it in 12 hours. If all three are opened, the tank fills in: Practice
Correct answer: (A)
Solution: Capacity = 120; rates +15, +8, −10 = 13/hour → 120/13 = 9.23 hours.
Solution: Capacity = 120; rates +15, +8, −10 = 13/hour → 120/13 = 9.23 hours.
Q5. Pipes A and B fill a tank in 15 and 20 minutes. Both are opened together and A is closed after 4 minutes. In how much total time will the tank fill? Practice
Correct answer: (B)
Solution: Capacity 60; 28 filled in 4 min; B fills the remaining 32 in 10.67 min; total 14.67 minutes.
Solution: Capacity 60; 28 filled in 4 min; B fills the remaining 32 in 10.67 min; total 14.67 minutes.
Q6. A tap fills water at 6 litres per minute into a tank of 900 litres. If the tank is half full, how many minutes are needed to fill it completely? Practice
Correct answer: (C)
Solution: Remaining = 900/2 = 450 L; time = 450/6 = 75 minutes.
Solution: Remaining = 900/2 = 450 L; time = 450/6 = 75 minutes.
Q7. Two pipes A and B can fill a tank in 15 and 8 hours. If both are opened together, how long will the tank take to fill? Practice
Correct answer: (D)
Solution: Time = ab/(a + b) = 15×8/23 = 5.22 hours.
Solution: Time = ab/(a + b) = 15×8/23 = 5.22 hours.
Q8. A pipe fills a tank in 5 hours, but due to a leak it takes 6 hours. In how much time will the leak alone empty the full tank? Practice
Correct answer: (A)
Solution: Leak = a(a + t)/t = 5×6/1 = 30 hours.
Solution: Leak = a(a + t)/t = 5×6/1 = 30 hours.
Q9. Pipes A and B fill a tank in 24 and 15 minutes. Both are opened together and A is closed after 5 minutes. In how much total time will the tank fill? Practice
Correct answer: (B)
Solution: Capacity 120; 65 filled in 5 min; B fills the remaining 55 in 6.88 min; total 11.88 minutes.
Solution: Capacity 120; 65 filled in 5 min; B fills the remaining 55 in 6.88 min; total 11.88 minutes.
Q10. A tap fills water at 8 litres per minute into a tank of 1440 litres. If the tank is half full, how many minutes are needed to fill it completely? Practice
Correct answer: (C)
Solution: Remaining = 1440/2 = 720 L; time = 720/8 = 90 minutes.
Solution: Remaining = 1440/2 = 720 L; time = 720/8 = 90 minutes.
Q11. Two pipes A and B can fill a tank in 4 and 5 hours. If both are opened together, how long will the tank take to fill? Practice
Correct answer: (D)
Solution: Time = ab/(a + b) = 4×5/9 = 2.22 hours.
Solution: Time = ab/(a + b) = 4×5/9 = 2.22 hours.
Q12. A pipe fills a tank in 12 hours, but due to a leak it takes 13 hours. In how much time will the leak alone empty the full tank? Practice
Correct answer: (A)
Solution: Leak = a(a + t)/t = 12×13/1 = 156 hours.
Solution: Leak = a(a + t)/t = 12×13/1 = 156 hours.
Q13. Pipes A and B fill a tank in 8 and 12 hours, while pipe C empties it in 24 hours. If all three are opened, the tank fills in: Practice
Correct answer: (B)
Solution: Capacity = 24; rates +3, +2, −1 = 4/hour → 24/4 = 6 hours.
Solution: Capacity = 24; rates +3, +2, −1 = 4/hour → 24/4 = 6 hours.
Q14. Pipes A and B fill a tank in 12 and 30 minutes. Both are opened together and A is closed after 5 minutes. In how much total time will the tank fill? Practice
Correct answer: (C)
Solution: Capacity 60; 35 filled in 5 min; B fills the remaining 25 in 12.5 min; total 17.5 minutes.
Solution: Capacity 60; 35 filled in 5 min; B fills the remaining 25 in 12.5 min; total 17.5 minutes.
Q15. A tap fills water at 4 litres per minute into a tank of 900 litres. If the tank is half full, how many minutes are needed to fill it completely? Practice
Correct answer: (D)
Solution: Remaining = 900/2 = 450 L; time = 450/4 = 112.5 minutes.
Solution: Remaining = 900/2 = 450 L; time = 450/4 = 112.5 minutes.
Q16. Pipes A and B can fill a tank in 12 and 16 minutes respectively. Both are opened together. After how many minutes should B be closed so that the tank is full in exactly 9 minutes? Practice
Correct answer: (A)
Solution: A works all 9 minutes and fills 9/12 = 3/4 of the tank; B fills the remaining 1/4 ⇒ B works 16 × 1/4 = 4 minutes.
Solution: A works all 9 minutes and fills 9/12 = 3/4 of the tank; B fills the remaining 1/4 ⇒ B works 16 × 1/4 = 4 minutes.
Q17. A pipe fills a tank in 6 hours, but due to a leak it takes 8 hours. In how much time will the leak alone empty the full tank? Practice
Correct answer: (B)
Solution: Leak = a(a + t)/t = 6×8/2 = 24 hours.
Solution: Leak = a(a + t)/t = 6×8/2 = 24 hours.
Q18. Pipes A and B fill a tank in 15 and 8 hours, while pipe C empties it in 30 hours. If all three are opened, the tank fills in: Practice
Correct answer: (C)
Solution: Capacity = 120; rates +8, +15, −4 = 19/hour → 120/19 = 6.32 hours.
Solution: Capacity = 120; rates +8, +15, −4 = 19/hour → 120/19 = 6.32 hours.
Q19. Pipes A and B fill a tank in 15 and 20 minutes. Both are opened together and A is closed after 2 minutes. In how much total time will the tank fill? Practice
Correct answer: (D)
Solution: Capacity 60; 14 filled in 2 min; B fills the remaining 46 in 15.33 min; total 17.33 minutes.
Solution: Capacity 60; 14 filled in 2 min; B fills the remaining 46 in 15.33 min; total 17.33 minutes.
Q20. A tap fills water at 10 litres per minute into a tank of 900 litres. If the tank is half full, how many minutes are needed to fill it completely? Practice
Correct answer: (A)
Solution: Remaining = 900/2 = 450 L; time = 450/10 = 45 minutes.
Solution: Remaining = 900/2 = 450 L; time = 450/10 = 45 minutes.