Multiple choice

P, Q and R start a business jointly. Twice the capital of P is equal to thrice the capital of Q and the capital Q is four times the capital of R, find the share of Q in an annual profit of ₹148500

  1. ₹54000

  2. ₹64000

  3. ₹56000

  4. ₹55000
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A Correct answer
Explanation

From the given conditions, we have 2P = 3Q and Q = 4R. Expressing all capitals in terms of Q gives P = 1.5Q and R = 0.25Q, which yields a investment ratio P : Q : R of 6 : 4 : 1. Q's share of the profit is therefore 4/11 of the total profit of Rs. 148,500, which equals Rs. 54,000.

AI explanation

The given conditions mean twice P equals three times Q, so P is 1.5 times Q; also, Q is four times R, meaning R is one-fourth of Q. This makes the ratio of capitals for P : Q : R equal to 1.5 : 1 : 0.25, which simplifies to 6 : 4 : 1. The total of 11 parts corresponds to the profit of Rs. 148500, so one part equals 148500 divided by 11, which is 13500; Q's share is 4 parts, giving 4 multiplied by 13500, which equals Rs. 54000.

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