Multiple choice

A, B and C were partners in a business. A was in partnership for 1 year 6 months, B was in partnership for 1 year 2 months and C was in partnership for half the time as A. If they shared the profit in ratio 3 : 7 : 11, then which of the following represents the ratio of their investments?

  1. 3 : 9 : 22

  2. 3 : 3 : 22

  3. 2 : 5 : 22

  4. 1 : 3 : 11

  5. None of these
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A Correct answer
Explanation

Profit = Investment * Time. Let investments be I_A, I_B, I_C. Time: A=18 months, B=14 months, C=9 months. Profit ratio: 3:7:11. I_A * 18 = 3k, I_B * 14 = 7k, I_C * 9 = 11k. I_A = 3k/18 = k/6. I_B = 7k/14 = k/2. I_C = 11k/9. Ratio: 1/6 : 1/2 : 11/9. Multiply by 18: 3 : 9 : 22.

AI explanation

Convert the time periods to months to get 18 months for A, 14 months for B, and 9 months for C. The ratio of profit equals the product of investment and time, so the ratio of investments is 3/18 : 7/14 : 11/9, which simplifies to 1/6 : 1/2 : 11/9. Multiplying by 18 gives the investment ratio of 3:9:22.

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