Three partners shared the profit in a business in the ratio 8:6:9. They had partnered for 9 months, 12 months and 6 months respectively. What was the ratio of their investments?

5:4:4

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27:9:16

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16:9:27

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1:2:3

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8:9:12

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Solution

The correct option is C
16:9:27

$\frac{I n v e s t m e n t o f A \times t i m e o f i n v e s t m e n t o f A}{I n v e s t m e n t o f B \times t i m e o f i n v e s t m e n t o f B}$ = $\frac{P r o f i t o f A}{P r o f i t o f B}$

Let the ratio of the investment of A:B = x:y

$\frac{x \times 9}{y \times 12} = \frac{8}{6}$

$\frac{x}{y} = \frac{16}{9}$

$\frac{y \times 12}{z \times 6} = \frac{6}{9}$

$\frac{y}{z} = \frac{1}{3} = \frac{9}{27}$

$x : y : z = 16 : 9 : 27$

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Three partners shared the profit in a business in the ratio 8:6:9. They had partnered for 9 months, 12 months and 6 months respectively. What was the ratio of their investments?

The correct option is C 16:9:27 Investment of A ×time of investment of AInvestment of B ×time of investment of B= Profit of AProfit of B Let the ratio of the investment of A:B = x:y x×9y×12=86 xy=169 y×12z×6=69 yz=13=927 x:y:z=16:9:27