Multiple choice

Ram and Shyam enter into a partnership with their share of capital in the ratio 5 : 8. Ram withdrew his money after six months and they divided the profit in the ratio 5 : 4 after one year. For how long was Shyam's capital used?

  1. 3 months

  2. 4 months

  3. 6 months

  4. 5 months
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A Correct answer
Explanation

Profit ratio = (Capital1 * Time1) / (Capital2 * Time2). 5/4 = (5 * 6) / (8 * T). 5/4 = 30 / 8T. 40T = 120. T = 3 months.

AI explanation

The formula for partnership profits is the ratio of the product of investment and time. Assuming Shyam's capital was used for the full twelve months, the effective capital ratio becomes (5 times 6) to (8 times 12), which is 30:96 or 5:16. Since the actual profit ratio given is 5:4, the assumption of twelve months is incorrect; instead, the ratio is (5 times 6) to (8 times time), yielding 30:8t. Solving 30/8t = 5/4 results in 8t = 24, which means Shyam's capital was used for 3 months.

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