A began a business with Rs. 85,000. He was joined afterwards by B with Rs.…
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A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
- A.
4 months
- B.
5 months
- C.
6 months
- D.
8 months
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Correct answer: D
Explanation: The profit share is proportional to capital multiplied by time. Let the time for which B joined be x months.
Compute A's capital-time: 85,000 × 12 = 1,020,000.
Compute B's capital-time: 42,500 × x = 42,500x.
Form the ratio A : B = 1,020,000 : 42,500x. Dividing both terms by 42,500 gives 24 : x.
This ratio must equal the given profit ratio 3 : 1, so 24 : x = 3 : 1. Solving gives x = 24 × (1/3) = 8.
Conclusion: B joined for 8 months.