Multiple choice

P, Q, and R started a business with investments in the ratio 20 : 15 : 12. After 3 months, R withdrew half of his investment, and after another 9 months, a profit of ₹323,000 was divided between them. R's profit share was

  1. 57,000rs

  2. 52,000rs

  3. 1,52,000rs

  4. 1,57,000rs

  5. 63,000rs
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A Correct answer
Explanation

Investment ratios: P=20, Q=15, R=12. P and Q invest for 12 months. R invests 12 for 3 months, then 6 for 9 months. Total units: P=240, Q=180, R=(36+54)=90. Ratio 240:180:90 = 8:6:3. Total parts = 17. R's share = (3/17) * 323000 = 3 * 19000 = 57000.

AI explanation

Using the partnership formula, the ratio of profits equals the ratio of the product of investments and time. Let the initial investments be 20x, 15x, and 12x; R's effective capital becomes (12x * 3) + (6x * 9) = 90x. The effective capital for P is 20x * 12 = 240x, and for Q it is 15x * 12 = 180x, making their profit ratio 240 : 180 : 90, which simplifies to 8 : 6 : 3. The total parts in the ratio is 17, so R's share out of the total profit of 323,000 is (3/17) * 323,000, resulting in 57,000 rs.

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