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P, Q and R begin a venture investing capital in the ratio 1 : 2 : 4. R takes back half of his capital after 4 months, and Q withdraws a quarter of his 2 months after that. The business runs for a full 12 months and earns a total profit of Rs 2,40,000. In what ratio is the profit shared among P, Q and R?

1. 32 : 21 : 12
2. 21 : 12 : 33
3. 12 : 21 : 32
4. 12 : 33 : 42

Correct answer: 12 : 21 : 32

Solution

Using capital-months: P = 1x12 = 12; Q = 2x6 + 1.5x6 = 21; R = 4x4 + 2x8 = 32. So the ratio is 12 : 21 : 32.

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