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Select the correct answerIn a partnership business, Q’s capital was half of P’s if after 8 months,Q withdrew half of his capital and after 2 months more P withdrew 1/4th of his capital, then the profit ratio of P and Q after 1 year will beOptions9 : 237 : 27 : 523 : 10

Question

Select the correct answerIn a partnership business, Q’s capital was half of P’s if after 8 months,Q withdrew half of his capital and after 2 months more P withdrew 1/4th of his capital, then the profit ratio of P and Q after 1 year will beOptions9 : 237 : 27 : 523 : 10

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Solution

The problem is about the distribution of profit in a partnership business. The profit is divided according to the capital invested and the time for which it was invested.

Let's denote P's capital as 2x (since Q's capital is half of P's, we denote Q's capital as x).

P's capital is invested for 10 months (8 months fully and 2 months 3/4th after he withdrew 1/4th of his capital). So, P's capital-time contribution is 2x*8 + (3/4)2x2 = 16x + 3x = 19x.

Q's capital is invested for 8 months fully and 4 months half (after he withdrew half of his capital). So, Q's capital-time contribution is x*8 + (1/2)x4 = 8x + 2x = 10x.

The profit ratio of P and Q is therefore 19x : 10x or 19 : 10.

So, the correct answer is 23 : 10.

This problem has been solved

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