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A, B and C start a business. If the ratio of their periods of investments are 2 : 3 : 5 and their profits are in the ratio of 6 : 7 : 10. Then what is the ratio of capitals?
- A9 : 7 : 6
- B3 : 11 : 2
- C3 : 5 : 7
- D5 : 8 : 9
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CCommunity
Let, A’s capital = A
Let, B’s capital = B
Let, C’s capital = C
Let, period of A’s investment = 2x
Let, period of B’s investment = 3x
Let, period of C’s investment = 5x
And,
Let, A’s profit = 6y
Let, B’s profit = 7y
Let, C’s profit = 10y
According to the problem,
A × 2x = 6y
⇒ A = 3y/x
B × 3x = 7y
⇒ B = 7y/3x
According to the problem,
C × 5x = 10y
⇒ C = 2y/x
∴ The ratio of capital is,
A : B : C = 3y/x : 7y/3x : 2y/x
⇒ 9 : 7 : 6
Let, B’s capital = B
Let, C’s capital = C
Let, period of A’s investment = 2x
Let, period of B’s investment = 3x
Let, period of C’s investment = 5x
And,
Let, A’s profit = 6y
Let, B’s profit = 7y
Let, C’s profit = 10y
According to the problem,
A × 2x = 6y
⇒ A = 3y/x
B × 3x = 7y
⇒ B = 7y/3x
According to the problem,
C × 5x = 10y
⇒ C = 2y/x
∴ The ratio of capital is,
A : B : C = 3y/x : 7y/3x : 2y/x
⇒ 9 : 7 : 6