Question
A invests Rs 6000 in a business for the whole year. B
joins him later with an investment of Rs 8000. At the end of the year, the profit is divided between A and B in the ratio 3 : 2. After how many months from the start did B join the business?Solution
Profit is shared in the ratio of (capital × time). A’s investment-time = 6000 × 12 = 72000 Let B join after x months, so he invests for (12 − x) months. But simpler: let B’s investment time be t months. B’s investment-time = 8000 × t Ratio: A : B = 72000 : 8000t = 3 : 2 Divide by 1000: 72 : 8t = 3 : 2 Cross-multiply: 72 × 2 = 3 × 8t 144 = 24t t = 6 So B was in business for 6 months, meaning he joined after 12 − 6 = 6 months from the start.
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