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Question

A, B and C invested capitals in the ratio 3:5:9; the timing of their investments being in the ratio 2 : 3 : 1. In what ratio would their profits be distributed?

A
2 : 5 : 3
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B
3 : 2 : 5
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C
7 : 5 : 3
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D
Insufficient data
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E
None of the above
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Solution

The correct option is A 2 : 5 : 3
Ratio of capitals of A, B and C is 3:5:9. Let the capitals of A, B and C be 3x, 5x and 9x, respectively.
Ratio of timing of their investments are 2:3:1. Let, A, B and C invest their capitals for 2y, 3y and y months, respectively.
Then, profit of A : profit of B : profit of C
=C1×t1:C2×t2:C3×t3
=3x×2y:5x×3y:9x×y
=6:15:9 or 2:5:3

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