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Select the correct answerA, B and C invested their capital in to a partnership business in the following manner. A invests one-half of the capital for three -fourth of the time. B invests one- third of the capital for one- half of the time and C invests the remaining capital for the whole time. If the profit earned is RS. 510, how much should A get?OptionsRS. 260RS. 300RS. 250RS. 270RS. 280

Question

Select the correct answerA, B and C invested their capital in to a partnership business in the following manner. A invests one-half of the capital for three -fourth of the time. B invests one- third of the capital for one- half of the time and C invests the remaining capital for the whole time. If the profit earned is RS. 510, how much should A get?OptionsRS. 260RS. 300RS. 250RS. 270RS. 280

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Solution

The profit distribution in a partnership is proportional to the capital invested and the time for which it was invested.

Let's denote the total capital as 'C' and the total time as 'T'.

  1. A invests one-half of the capital for three-fourths of the time. So, A's share is (1/2)C * (3/4)T = (3/8)CT
  2. B invests one-third of the capital for one-half of the time. So, B's share is (1/3)C * (1/2)T = (1/6)CT
  3. C invests the remaining capital for the whole time. The remaining capital is C - (1/2)C - (1/3)C = (1/6)C. So, C's share is (1/6)C * T = (1/6)CT

The total profit is RS. 510, which is divided according to the shares of A, B, and C.

The total share is (3/8)CT + (1/6)CT + (1/6)CT = (5/8)CT

So, A's part of the profit is (A's share / total share) * total profit = ((3/8)CT / (5/8)CT) * 510 = (3/5) * 510 = RS. 306

However, this option is not available in the given options. There might be a mistake in the question or the options provided.

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