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Select the correct answerP and Q started a business by investing their capitals in to ratio of 4:9. After 3 months P increased his capital to 1 ½ times. After 5 more months Q with draw 1/3 of capital. If they got RS. 5400 as the annual profit. Find the share of P in the profit.OptionsRS. 2600RS. 2700RS. 2400RS. 2200RS. 2800

Question

Select the correct answerP and Q started a business by investing their capitals in to ratio of 4:9. After 3 months P increased his capital to 1 ½ times. After 5 more months Q with draw 1/3 of capital. If they got RS. 5400 as the annual profit. Find the share of P in the profit.OptionsRS. 2600RS. 2700RS. 2400RS. 2200RS. 2800

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Solution

To solve this problem, we need to calculate the capital invested by P and Q over the year, and then divide the profit proportionally.

  1. P's initial capital is 4x and Q's initial capital is 9x. For the first 3 months, P and Q invested 4x3 and 9x3 respectively.

  2. After 3 months, P increased his capital to 1 ½ times, so his capital became 4x1.5 = 6x. For the next 5 months, P and Q invested 6x5 and 9x*5 respectively.

  3. After 8 months, Q withdrew 1/3 of his capital, so his capital became 9x*(2/3) = 6x. For the remaining 4 months, P and Q invested 6x4 and 6x4 respectively.

  4. The total capital invested by P over the year is 4x3 + 6x5 + 6x4 = 12x + 30x + 24x = 66x. The total capital invested by Q over the year is 9x3 + 9x5 + 6x4 = 27x + 45x + 24x = 96x.

  5. The total capital invested by both P and Q over the year is 66x + 96x = 162x. The share of P in the profit is (66x / 162x) * 5400 = RS. 2200.

So, the correct answer is RS. 2200.

This problem has been solved

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