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. 280RS. 260RS. 250RS. 300RS. 270
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. 280RS. 260RS. 250RS. 300RS. 270
Solution
To solve this problem, we need to understand the concept of partnership. In a partnership, profit is divided according to the ratio of capital invested and the time for which the capital is invested. This is often referred to as the Capital-Time (C-T) ratio.
Let's assume the total capital invested is 'P' and the total time is 'T'.
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A invests one-half of the capital for three-fourth of the time. So, A's C-T ratio is (1/2)P * (3/4)T = (3/8)PT.
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B invests one-third of the capital for one-half of the time. So, B's C-T ratio is (1/3)P * (1/2)T = (1/6)PT.
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C invests the remaining capital for the whole time. The remaining capital is (1 - 1/2 - 1/3)P = (1/6)P. So, C's C-T ratio is (1/6)P * T = (1/6)PT.
The total C-T ratio is (3/8 + 1/6 + 1/6)PT = (4/6)PT = (2/3)PT.
The profit is divided according to the C-T ratio. So, A's share of the profit is (A's C-T ratio / total C-T ratio) * total profit.
Therefore, A's share of the profit is [(3/8)PT / (2/3)PT] * 510 = (9/16) * 510 = RS. 286.875.
However, this is not one of the options given. It's possible that there's a mistake in the problem or the options. Please check the problem and the options again.
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