📑 Topics on this page (Jump to Topic):
📌 1. Basic Rules
📘 Formulas:
- Profit ratio = capital × time ratio: C₁T₁ : C₂T₂ : C₃T₃
- If time is the same, profit ratio = capital ratio
- If capital changes, add capital × months for each period
✏️ Example: A invests ₹3000 for 12 months and B ₹4000 for 9 months → 36000 : 36000 = 1 : 1.
📌 2. Working Partner & Special Cases
- The working partner first gets salary/commission; the remaining profit is shared in the investment ratio.
- If profit ratio and times are given, capital ratio = profit/time.
⚠️ Exam Traps:
- For "at the end of the year", count fewer months for a partner who joined later.
📌 3. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. A starts a business with ₹5000. After 4 months B joins with ₹10000. At the end of the year, B's share of a profit of ₹1750 is: Practice
Correct answer: (B)
Solution: A : B = 5000×12 : 10000×8 = 3 : 4; B = 1750 × 4/7 = ₹1000.
Solution: A : B = 5000×12 : 10000×8 = 3 : 4; B = 1750 × 4/7 = ₹1000.
Q2. A and B share profit in the ratio 4 : 3; their capitals were invested for 4 and 10 months. The ratio of their capitals is: Practice
Correct answer: (C)
Solution: Capital ∝ profit/time: 4/4 : 3/10 = 10 : 3.
Solution: Capital ∝ profit/time: 4/4 : 3/10 = 10 : 3.
Q3. A and B invest ₹4000 and ₹6000. After 6 months, A withdraws ₹1000. The profit ratio (A : B) at the end of the year is: Practice
Correct answer: (D)
Solution: A = 4000×6 + 3000×6 = 42000; B = 6000×12 = 72000 → 7 : 12.
Solution: A = 4000×6 + 3000×6 = 42000; B = 6000×12 = 72000 → 7 : 12.
Q4. A starts a business with ₹3000. B joins later and his capital stays for 6 months. Profit at year-end is shared 3 : 2. B's capital is: Practice
Correct answer: (A)
Solution: 3000×12 : B×6 = 3 : 2 → B = 3000×12×2/(3×6) = ₹4000.
Solution: 3000×12 : B×6 = 3 : 2 → B = 3000×12×2/(3×6) = ₹4000.
Q5. A, B and C start a business investing ₹3000, ₹4000 and ₹9000. At the end of the year the profit is ₹7200. B's share is: Practice
Correct answer: (B)
Solution: Ratio = 3 : 4 : 9; B = 7200 × 4/16 = ₹1800.
Solution: Ratio = 3 : 4 : 9; B = 7200 × 4/16 = ₹1800.
Q6. A starts a business with ₹3000. After 6 months B joins with ₹9000. At the end of the year, B's share of a profit of ₹1000 is: Practice
Correct answer: (C)
Solution: A : B = 3000×12 : 9000×6 = 2 : 3; B = 1000 × 3/5 = ₹600.
Solution: A : B = 3000×12 : 9000×6 = 2 : 3; B = 1000 × 3/5 = ₹600.
Q7. A and B share profit in the ratio 5 : 4; their capitals were invested for 12 and 8 months. The ratio of their capitals is: Practice
Correct answer: (D)
Solution: Capital ∝ profit/time: 5/12 : 4/8 = 5 : 6.
Solution: Capital ∝ profit/time: 5/12 : 4/8 = 5 : 6.
Q8. A and B invest in the ratio 2 : 3. A is the working partner and gets 10% of the profit for managing; the rest is shared in the capital ratio. Out of a profit of ₹10000, A gets in all: Practice
Correct answer: (A)
Solution: Management = ₹1000; 2/5 of remaining ₹9000 = ₹3600; total = ₹4600.
Solution: Management = ₹1000; 2/5 of remaining ₹9000 = ₹3600; total = ₹4600.
Q9. A and B invest ₹6000 and ₹8000. After 3 months, A withdraws ₹1000. The profit ratio (A : B) at the end of the year is: Practice
Correct answer: (B)
Solution: A = 6000×3 + 5000×9 = 63000; B = 8000×12 = 96000 → 21 : 32.
Solution: A = 6000×3 + 5000×9 = 63000; B = 8000×12 = 96000 → 21 : 32.
Q10. A starts a business with ₹5000. B joins later and his capital stays for 8 months. Profit at year-end is shared 2 : 1. B's capital is: Practice
Correct answer: (C)
Solution: 5000×12 : B×8 = 2 : 1 → B = 5000×12×1/(2×8) = ₹3750.
Solution: 5000×12 : B×8 = 2 : 1 → B = 5000×12×1/(2×8) = ₹3750.
Q11. A starts a business with ₹8000. After 3 months B joins with ₹10000. At the end of the year, B's share of a profit of ₹6200 is: Practice
Correct answer: (D)
Solution: A : B = 8000×12 : 10000×9 = 16 : 15; B = 6200 × 15/31 = ₹3000.
Solution: A : B = 8000×12 : 10000×9 = 16 : 15; B = 6200 × 15/31 = ₹3000.
Q12. A and B share profit in the ratio 3 : 5; their capitals were invested for 4 and 10 months. The ratio of their capitals is: Practice
Correct answer: (A)
Solution: Capital ∝ profit/time: 3/4 : 5/10 = 3 : 2.
Solution: Capital ∝ profit/time: 3/4 : 5/10 = 3 : 2.
Q13. A and B invest ₹10000 and ₹6000. After 4 months, A withdraws ₹3000. The profit ratio (A : B) at the end of the year is: Practice
Correct answer: (B)
Solution: A = 10000×4 + 7000×8 = 96000; B = 6000×12 = 72000 → 4 : 3.
Solution: A = 10000×4 + 7000×8 = 96000; B = 6000×12 = 72000 → 4 : 3.
Q14. A starts a business with ₹6000. B joins later and his capital stays for 4 months. Profit at year-end is shared 2 : 1. B's capital is: Practice
Correct answer: (C)
Solution: 6000×12 : B×4 = 2 : 1 → B = 6000×12×1/(2×4) = ₹9000.
Solution: 6000×12 : B×4 = 2 : 1 → B = 6000×12×1/(2×4) = ₹9000.
Q15. A starts a business with ₹6000. After 3 months B joins with ₹6000. At the end of the year, B's share of a profit of ₹700 is: Practice
Correct answer: (D)
Solution: A : B = 6000×12 : 6000×9 = 4 : 3; B = 700 × 3/7 = ₹300.
Solution: A : B = 6000×12 : 6000×9 = 4 : 3; B = 700 × 3/7 = ₹300.
Q16. A and B share profit in the ratio 2 : 3; their capitals were invested for 10 and 6 months. The ratio of their capitals is: Practice
Correct answer: (A)
Solution: Capital ∝ profit/time: 2/10 : 3/6 = 2 : 5.
Solution: Capital ∝ profit/time: 2/10 : 3/6 = 2 : 5.
Q17. A and B invest in the ratio 1 : 2. A is the working partner and gets 10% of the profit for managing; the rest is shared in the capital ratio. Out of a profit of ₹15000, A gets in all: Practice
Correct answer: (B)
Solution: Management = ₹1500; 1/3 of remaining ₹13500 = ₹4500; total = ₹6000.
Solution: Management = ₹1500; 1/3 of remaining ₹13500 = ₹4500; total = ₹6000.
Q18. A and B invest ₹10000 and ₹8000. After 3 months, A withdraws ₹3000. The profit ratio (A : B) at the end of the year is: Practice
Correct answer: (C)
Solution: A = 10000×3 + 7000×9 = 93000; B = 8000×12 = 96000 → 31 : 32.
Solution: A = 10000×3 + 7000×9 = 93000; B = 8000×12 = 96000 → 31 : 32.
Q19. A starts a business with ₹6000. B joins later and his capital stays for 4 months. Profit at year-end is shared 3 : 2. B's capital is: Practice
Correct answer: (D)
Solution: 6000×12 : B×4 = 3 : 2 → B = 6000×12×2/(3×4) = ₹12000.
Solution: 6000×12 : B×4 = 3 : 2 → B = 6000×12×2/(3×4) = ₹12000.
Q20. A and B invest in the ratio 1 : 2. A is the working partner and gets 15% of the profit for managing; the rest is shared in the capital ratio. Out of a profit of ₹18000, A gets in all: Practice
Correct answer: (A)
Solution: Management = ₹2700; 1/3 of remaining ₹15300 = ₹5100; total = ₹7800.
Solution: Management = ₹2700; 1/3 of remaining ₹15300 = ₹5100; total = ₹7800.