Multiple choice

Four friends P, Q, R and S started a business in partnership. P's and Q's investments are Rs. 10,000 and 20,000, respectively. R's investment is the average of the investments of P and Q. S's investment is 20% more than P's. P withdraws 50% of his investment after 6 months. The profit at the end of the year is distributed in the ratio of their investments. If the profit of S is Rs. 97,200, then what is the profit share of Q?

  1. Rs. 1,62,000

  2. Rs. 1,52,000

  3. Rs. 1,42,000

  4. Rs. 1,65,000

  5. Rs. 1,74,000
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A Correct answer
Explanation

Investments (in thousands): P=10, Q=20, R=15, S=12. P's effective investment: (10*6 + 5*6)/12 = 7.5. Q=20, R=15, S=12. Ratio P:Q:R:S = 7.5:20:15:12 = 15:40:30:24. If S's profit (24 parts) = 97200, then 1 part = 4050. Q's profit = 40 * 4050 = 162000.

AI explanation

P's effective investment is 10000 for 6 months plus 5000 for 6 months, equaling 90000, while Q's is 20000*12 = 240000, R's is 15000*12 = 180000, and S's is 12000*12 = 144000, giving an effective ratio of 90:240:180:144 or 15:40:30:24. Since S's profit of 97200 corresponds to 24 parts, one part equals 97200 divided by 24, which is 4050. Q's profit share of 40 parts is therefore 40*4050 = 162000.

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