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werIn 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 beOptions7 : 27 : 59 : 2323 : 10

Question

werIn 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 beOptions7 : 27 : 59 : 2323 : 10

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Solution

The problem is about the distribution of profit in a partnership based on the capital contribution and the time for which the capital 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).

  1. For the first 8 months, P's capital is 2x and Q's capital is x.
  2. After 8 months, Q withdraws half of his capital, so his capital becomes x/2. P's capital remains 2x. This situation lasts for 2 months.
  3. After 10 months (8+2), P withdraws 1/4 of his capital, so his capital becomes 2x - 2x/4 = 1.5x. Q's capital remains x/2. This situation lasts for 2 months (12-10).

The profit of each partner is directly proportional to the product of the capital invested and the time for which it was invested.

So, P's share in the profit = 2x8 (for the first 8 months) + 2x2 (for the next 2 months) + 1.5x*2 (for the last 2 months) = 16x + 4x + 3x = 23x.

Q's share in the profit = x8 (for the first 8 months) + x/22 (for the next 2 months) + x/2*2 (for the last 2 months) = 8x + x + x = 10x.

Therefore, the profit ratio of P and Q after 1 year will be 23:10.

This problem has been solved

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