Multiple choice

A and B begin a partnership firm with capitals in the ratio 7 : 9. At the end of 9 months, A withdraws. If they receive profits in the ratio of 7 : 9, find how long B's capital was used?

  1. 6 months

  2. 7 months

  3. 8 months

  4. 9 months
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D Correct answer
Explanation

Profit ratio = (Capital A * Time A) / (Capital B * Time B). 7/9 = (7 * 9) / (9 * T). 7/9 = 63 / (9T). 63T = 567, T = 9 months.

AI explanation

Using the partnership formula, the ratio of profits is the ratio of the product of capital and time, so 7:9 equals (7 multiplied by 9) divided by (9 multiplied by B's time). This simplifies to 1 divided by B's time equals 1 divided by 9. Therefore, B's capital was used for 9 months.

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