This lesson gives one rule, the reason it works and seven worked examples. It also lists the traps that cost marks.
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Q1. A partner who only invests money without participating in management is called what?
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Answer: C
A sleeping partner contributes capital to the business only. This partner takes no part in daily management or decisions. Only a working partner manages operations; a sleeping partner does not. Profit is still shared based on the capital each partner invested.
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Q2. A partner who manages the business, in addition to investing money, is called what?
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Answer: A
A working partner puts capital into the business, like any partner. In addition, this partner takes an active role in running it day to day. This is different from a sleeping partner, who only supplies capital. Because of the extra effort, a working partner may also draw a salary.
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Q3. In a compound partnership, where partners invest for different time periods, the equivalent capital for each partner is computed as what?
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Answer: B
In a compound partnership, partners invest for different lengths of time. Capital alone cannot be compared fairly when durations differ. So each partner’s capital is weighted by the time it stayed invested. Equivalent capital = capital multiplied by the number of time units invested. This equivalent capital, not the raw capital, decides each partner’s profit share.
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Q4. In a simple partnership, where all capitals are invested for the same time, gain or loss is divided in what ratio?
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Answer: A
In a simple partnership, every partner invests for the same length of time. Because time is equal for everyone, it does not affect the split. So gain or loss depends only on how much capital each partner put in. This means profit or loss is divided in the ratio of the investments.
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Q5. Afzal and Amit are partners in a business, sharing profits in the ratio 3:4. If Afzal’s investment is Rs. 21000, what is Amit’s investment?
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Answer: C
Let Afzal’s investment = Rs. 21000 and Amit’s investment = I (unknown). Profit-sharing ratio = 3:4, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 3/4. That gives 21000 / I = 3/4. Solve for I: I = (4/3) x 21000 = 28000. Check: 21000:28000 simplifies to 3:4, matching the given ratio.
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Q6. Afzal and Amit are partners in a business, sharing profits in the ratio 4:9. If Afzal’s investment is Rs. 25000, what is Amit’s investment?
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Answer: D
Let Afzal’s investment = Rs. 25000 and Amit’s investment = I (unknown). Profit-sharing ratio = 4:9, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 4/9. That gives 25000 / I = 4/9. Solve for I: I = (9/4) x 25000 = 56250. Check: 25000:56250 simplifies to 4:9, matching the given ratio.
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Q7. Afzal and Amit are partners in a business, sharing profits in the ratio 1:2. If Afzal’s investment is Rs. 38000, what is Amit’s investment?
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Answer: C
Let Afzal’s investment = Rs. 38000 and Amit’s investment = I (unknown). Profit-sharing ratio = 1:2, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 1/2. That gives 38000 / I = 1/2. Solve for I: I = (2/1) x 38000 = 76000. Check: 38000:76000 simplifies to 1:2, matching the given ratio.
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Q8. Afzal and Amit are partners in a business, sharing profits in the ratio 8:5. If Afzal’s investment is Rs. 6000, what is Amit’s investment?
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Answer: B
Let Afzal’s investment = Rs. 6000 and Amit’s investment = I (unknown). Profit-sharing ratio = 8:5, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 8/5. That gives 6000 / I = 8/5. Solve for I: I = (5/8) x 6000 = 3750. Check: 6000:3750 simplifies to 8:5, matching the given ratio.
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Q9. Afzal and Amit are partners in a business, sharing profits in the ratio 10:9. If Afzal’s investment is Rs. 27000, what is Amit’s investment?
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Answer: A
Let Afzal’s investment = Rs. 27000 and Amit’s investment = I (unknown). Profit-sharing ratio = 10:9, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 10/9. That gives 27000 / I = 10/9. Solve for I: I = (9/10) x 27000 = 24300. Check: 27000:24300 simplifies to 10:9, matching the given ratio.
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Q10. Afzal and Amit are partners in a business, sharing profits in the ratio 3:4. If Afzal’s investment is Rs. 30000, what is Amit’s investment?
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Answer: D
Let Afzal’s investment = Rs. 30000 and Amit’s investment = I (unknown). Profit-sharing ratio = 3:4, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 3/4. That gives 30000 / I = 3/4. Solve for I: I = (4/3) x 30000 = 40000. Check: 30000:40000 simplifies to 3:4, matching the given ratio.
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Q11. Afzal and Amit are partners in a business, sharing profits in the ratio 2:3. If Afzal’s investment is Rs. 32000, what is Amit’s investment?
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Answer: C
Let Afzal’s investment = Rs. 32000 and Amit’s investment = I (unknown). Profit-sharing ratio = 2:3, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 2/3. That gives 32000 / I = 2/3. Solve for I: I = (3/2) x 32000 = 48000. Check: 32000:48000 simplifies to 2:3, matching the given ratio.
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Q12. Afzal and Amit are partners in a business, sharing profits in the ratio 4:3. If Afzal’s investment is Rs. 32000, what is Amit’s investment?
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Answer: B
Let Afzal’s investment = Rs. 32000 and Amit’s investment = I (unknown). Profit-sharing ratio = 4:3, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 4/3. That gives 32000 / I = 4/3. Solve for I: I = (3/4) x 32000 = 24000. Check: 32000:24000 simplifies to 4:3, matching the given ratio.
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Q13. Afzal and Amit are partners in a business, sharing profits in the ratio 4:3. If Afzal’s investment is Rs. 12000, what is Amit’s investment?
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Answer: A
Let Afzal’s investment = Rs. 12000 and Amit’s investment = I (unknown). Profit-sharing ratio = 4:3, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 4/3. That gives 12000 / I = 4/3. Solve for I: I = (3/4) x 12000 = 9000. Check: 12000:9000 simplifies to 4:3, matching the given ratio.
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Q14. Afzal and Amit are partners in a business, sharing profits in the ratio 2:1. If Afzal’s investment is Rs. 15000, what is Amit’s investment?
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Answer: D
Let Afzal’s investment = Rs. 15000 and Amit’s investment = I (unknown). Profit-sharing ratio = 2:1, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 2/1. That gives 15000 / I = 2/1. Solve for I: I = (1/2) x 15000 = 7500. Check: 15000:7500 simplifies to 2:1, matching the given ratio.
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Q15. Afzal and Amit are partners in a business, sharing profits in the ratio 3:5. If Afzal’s investment is Rs. 9000, what is Amit’s investment?
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Answer: D
Let Afzal’s investment = Rs. 9000 and Amit’s investment = I (unknown). Profit-sharing ratio = 3:5, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 3/5. That gives 9000 / I = 3/5. Solve for I: I = (5/3) x 9000 = 15000. Check: 9000:15000 simplifies to 3:5, matching the given ratio.
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Q16. Afzal and Amit are partners in a business, sharing profits in the ratio 1:4. If Afzal’s investment is Rs. 4000, what is Amit’s investment?
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Answer: C
Let Afzal’s investment = Rs. 4000 and Amit’s investment = I (unknown). Profit-sharing ratio = 1:4, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 1/4. That gives 4000 / I = 1/4. Solve for I: I = (4/1) x 4000 = 16000. Check: 4000:16000 simplifies to 1:4, matching the given ratio.
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Q17. Afzal and Amit are partners in a business, sharing profits in the ratio 8:5. If Afzal’s investment is Rs. 11000, what is Amit’s investment?
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Answer: B
Let Afzal’s investment = Rs. 11000 and Amit’s investment = I (unknown). Profit-sharing ratio = 8:5, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 8/5. That gives 11000 / I = 8/5. Solve for I: I = (5/8) x 11000 = 6875. Check: 11000:6875 simplifies to 8:5, matching the given ratio.
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Q18. Afzal and Amit are partners in a business, sharing profits in the ratio 5:6. If Afzal’s investment is Rs. 9000, what is Amit’s investment?
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Answer: A
Let Afzal’s investment = Rs. 9000 and Amit’s investment = I (unknown). Profit-sharing ratio = 5:6, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 5/6. That gives 9000 / I = 5/6. Solve for I: I = (6/5) x 9000 = 10800. Check: 9000:10800 simplifies to 5:6, matching the given ratio.
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Q19. Afzal and Amit are partners in a business, sharing profits in the ratio 2:1. If Afzal’s investment is Rs. 16000, what is Amit’s investment?
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Answer: A
Let Afzal’s investment = Rs. 16000 and Amit’s investment = I (unknown). Profit-sharing ratio = 2:1, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 2/1. That gives 16000 / I = 2/1. Solve for I: I = (1/2) x 16000 = 8000. Check: 16000:8000 simplifies to 2:1, matching the given ratio.
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Q20. Afzal and Amit are partners in a business, sharing profits in the ratio 2:3. If Afzal’s investment is Rs. 8000, what is Amit’s investment?
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Answer: B
Let Afzal’s investment = Rs. 8000 and Amit’s investment = I (unknown). Profit-sharing ratio = 2:3, and this ratio equals the investment ratio. So Afzal’s investment / Amit’s investment = 2/3. That gives 8000 / I = 2/3. Solve for I: I = (3/2) x 8000 = 12000. Check: 8000:12000 simplifies to 2:3, matching the given ratio.
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Q21. Meera started a business investing Rs. 24000. After 7 months, Rajesh joined with a capital of Rs. 40000. At the end of the year, they made a profit of Rs. 1403. What is Rajesh’s share?
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Answer: D
Let Meera invest Rs. 24000 for the full year, so Meera’s time = 12 months. Rajesh joined after 7 months, investing Rs. 40000. So Rajesh’s time = 12 – 7 = 5 months. Meera’s equivalent capital = 24000 x 12 = 288000. Rajesh’s equivalent capital = 40000 x 5 = 200000. Ratio of equivalent capitals = 288000:200000, which simplifies to 36:25. Rajesh’s share = 25/61 x Rs. 1403 = Rs. 575. Check: Meera’s share = 36/61 x Rs. 1403 = Rs. 828. Rs. 828 plus Rs. 575 equals Rs. 1403, the full profit.
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Q22. Meera started a business investing Rs. 8000. After 4 months, Rajesh joined with a capital of Rs. 7000. At the end of the year, they made a profit of Rs. 475. What is Rajesh’s share?
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Answer: C
Let Meera invest Rs. 8000 for the full year, so Meera’s time = 12 months. Rajesh joined after 4 months, investing Rs. 7000. So Rajesh’s time = 12 – 4 = 8 months. Meera’s equivalent capital = 8000 x 12 = 96000. Rajesh’s equivalent capital = 7000 x 8 = 56000. Ratio of equivalent capitals = 96000:56000, which simplifies to 12:7. Rajesh’s share = 7/19 x Rs. 475 = Rs. 175. Check: Meera’s share = 12/19 x Rs. 475 = Rs. 300. Rs. 300 plus Rs. 175 equals Rs. 475, the full profit.
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Q23. Meera started a business investing Rs. 30000. After 7 months, Rajesh joined with a capital of Rs. 44000. At the end of the year, they made a profit of Rs. 29. What is Rajesh’s share?
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Answer: D
Let Meera invest Rs. 30000 for the full year, so Meera’s time = 12 months. Rajesh joined after 7 months, investing Rs. 44000. So Rajesh’s time = 12 – 7 = 5 months. Meera’s equivalent capital = 30000 x 12 = 360000. Rajesh’s equivalent capital = 44000 x 5 = 220000. Ratio of equivalent capitals = 360000:220000, which simplifies to 18:11. Rajesh’s share = 11/29 x Rs. 29 = Rs. 11. Check: Meera’s share = 18/29 x Rs. 29 = Rs. 18. Rs. 18 plus Rs. 11 equals Rs. 29, the full profit.
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Q24. Meera started a business investing Rs. 30000. After 5 months, Rajesh joined with a capital of Rs. 13000. At the end of the year, they made a profit of Rs. 12177. What is Rajesh’s share?
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Answer: A
Let Meera invest Rs. 30000 for the full year, so Meera’s time = 12 months. Rajesh joined after 5 months, investing Rs. 13000. So Rajesh’s time = 12 – 5 = 7 months. Meera’s equivalent capital = 30000 x 12 = 360000. Rajesh’s equivalent capital = 13000 x 7 = 91000. Ratio of equivalent capitals = 360000:91000, which simplifies to 360:91. Rajesh’s share = 91/451 x Rs. 12177 = Rs. 2457. Check: Meera’s share = 360/451 x Rs. 12177 = Rs. 9720. Rs. 9720 plus Rs. 2457 equals Rs. 12177, the full profit.
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Q25. Meera started a business investing Rs. 48000. After 7 months, Rajesh joined with a capital of Rs. 14000. At the end of the year, they made a profit of Rs. 9690. What is Rajesh’s share?
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Answer: C
Let Meera invest Rs. 48000 for the full year, so Meera’s time = 12 months. Rajesh joined after 7 months, investing Rs. 14000. So Rajesh’s time = 12 – 7 = 5 months. Meera’s equivalent capital = 48000 x 12 = 576000. Rajesh’s equivalent capital = 14000 x 5 = 70000. Ratio of equivalent capitals = 576000:70000, which simplifies to 288:35. Rajesh’s share = 35/323 x Rs. 9690 = Rs. 1050. Check: Meera’s share = 288/323 x Rs. 9690 = Rs. 8640. Rs. 8640 plus Rs. 1050 equals Rs. 9690, the full profit.
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