Multiple choice

P and Q started a business and investment of Q is 25% more than that of P. After six months P doubled his investment and Q withdrew 1/3rd of his investment. If at the end of a year total profit obtained by them is Rs. 12200, then find the profit share of P?

  1. 4800

  2. 7200

  3. 6700

  4. 2300

  5. 1200
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B Correct answer
Explanation

P's investment: P*6 + 2P*6 = 18P. Q's investment: 1.25P*6 + (1.25P - 1/3*1.25P)*6 = 7.5P + 5P = 12.5P. Ratio P:Q = 18:12.5 = 36:25. Total parts = 61. P's share = (36/61) * 12200 = 36 * 200 = 7200.

AI explanation

Let P's investment be x, making Q's investment 1.25x. The profit ratio is determined by multiplying each investment by its duration, so P's ratio is 6x + 12x = 18x, while Q's ratio is 7.5x for the first 6 months and 2/3 of 1.25x (0.833x) for the next 6 months, totaling 8.333x. This results in a profit sharing ratio of 18 to 8.333, which simplifies to 36:17. P's profit share is calculated by multiplying the total profit of 12,200 by the fraction 36/53, resulting in a profit share of 7,200 for P.

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