A and B are partners in a business. A contributes 1/4 of the capital for 15…
2024
A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?
- A.
3 months
- B.
6 months
- C.
10 months
- D.
12 months
Attempted by 15 students.
Show answer & explanation
Correct answer: C
Key idea: profit is shared in proportion to capital × time.
Let total capital be 1 unit. A contributes 1/4, so B contributes 3/4.
A's capital × time = (1/4) × 15 = 15/4.
Let x be the number of months B's money is used. B's capital × time = (3/4) × x.
B receives two-thirds of the profit, so the ratio of B's share to A's share is 2:1. Therefore (3/4)x = 2 × (15/4).
Solve: multiply both sides by 4 to get 3x = 30, so x = 10 months.
Answer: B's money was used for 10 months.