Question
A and B start a business with investments of Rs 24,000 and Rs 36,000 respectively. After 6 months, C joins them with an investment of Rs 30,000. They share the profit at the end of the year in proportion to the product of capital and time. If the total annual profit is Rs 42,000, what is B’s share in the profit?
Solution
Capitals × time (in months): A: 24,000 for 12 months → 24,000 × 12 = 2,88,000 B: 36,000 for 12 months → 36,000 × 12 = 4,32,000 C: 30,000 for 6 months → 30,000 × 6 = 1,80,000 Ratio A : B : C = 2,88,000 : 4,32,000 : 1,80,000 Divide by 6,000: A : B : C = 48 : 72 : 30 Divide by 6: A : B : C = 8 : 12 : 5 Total parts = 8 + 12 + 5 = 25 Each part of profit = 42,000 / 25 = 1,680 B’s share = 12 × 1,680 = 20,160 rupees.
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