Multiple choice

A and B are partners in a business. A contributed 1/4th of the capital for 15 months and B received 2/3rd of the profit. For how much time (in months) was B's money used?

  1. 6 months

  2. 9 months

  3. 10 months

  4. 12 months
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total capital be C and total profit be P. A's capital = C/4, B's capital = 3C/4. A's time = 15 months. Let B's time = T. Profit ratio A:B = (C/4 * 15) : (3C/4 * T) = 15 : 3T = 5 : T. Given B's share is 2/3, A's share is 1/3. So 5/T = (1/3) / (2/3) = 1/2. T = 10 months.

AI explanation

Because B received 2/3 of the profit, A must have received 1/3, making their profit ratio 1 to 2. Since A contributed 1/4 of the capital, B contributed 3/4, making their capital ratio 1 to 3. Using the partnership formula, 1/2 equals (1 multiplied by 15) divided by (3 multiplied by B's time). Solving this equation gives 3 multiplied by B's time equals 30, which means B's money was used for 10 months. The correct answer is 10 months.

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