Mansi started a business investing Rs.42,000/-. After 7 months Kamya joined…
2025
Mansi started a business investing Rs.42,000/-. After 7 months Kamya joined her with a capital of Rs. 50,000/-. At the end of the year the total profit was Rs. 30,160/-. What is the share of profit of Kamya?
- A.
Rs. 10,000/-
- B.
Rs. 20,160/-
- C.
Rs. 10,160/-
- D.
Rs. 8,000/-
Show answer & explanation
Correct answer: A
Concept:
When partners invest different amounts of capital for different lengths of time, the profit is divided in the ratio of their "capital × time" (capital-months) invested, not merely in the ratio of the capital amounts.
Application:
Mansi invested Rs. 42,000/- for the full year, i.e. 12 months, so her capital-months = 42,000 × 12 = 5,04,000.
Kamya joined 7 months after the business started, so she invested for the remaining 12 − 7 = 5 months, so her capital-months = 50,000 × 5 = 2,50,000.
The profit-sharing ratio is 5,04,000 : 2,50,000, which simplifies to 252 : 125 (dividing both terms by 2,000).
The sum of the ratio parts is 252 + 125 = 377.
Kamya's share of the total profit of Rs. 30,160/- is (125/377) × 30,160 = 125 × 80 = Rs. 10,000/-.
Cross-check:
Mansi's share works out to (252/377) × 30,160 = Rs. 20,160/-, and 20,160 + 10,000 = 30,160, which equals the total profit — confirming the ratio was applied correctly.