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1. The ratio of investments of two partners X and Y is 11 : 12 and the ratio of their profit is 2 : 3. If X invested the money for 8 months, then the time for which Y invested the money is ?

A. 8 months

B. 9 months

C. 10 months

D. 11 months

Solution:

Let capital of X be Rs. 11x and Y's capital be Rs. 12x
and let time for which Y invested capital is T₂ months
by using formula,

\begin{aligned} \Leftrightarrow \frac{C_{1} \times T_{1}}{C_{2} \times T_{2}} = \frac{P_{1}}{P_{2}} \\ \Leftrightarrow \frac{11 x \times 8}{12 x \times T_{2}} = \frac{2}{3} \\ \Leftrightarrow T_{2} = 11 months \end{aligned}

Hence the time for which Y invested his capital is 11 months

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