X and Y are partners in a business. X contributed $\Large\frac{1}{3}$ of the capital for 9 months and Y received $\Large\frac{2}{5}$ of the profit. For how long was Y’s money used in the business ?

A. 2 months B. 3 months C. 4 months D. 5 months Answer: Option B
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Solution(By Apex Team)

$\begin{aligned}&\text{Let the total profit be Rs. x}\\ &\text{Then,}\\ &\text{Y’s share = Rs.}\frac{2z}{5}\\ &\text{X’s share = Rs.}\left(z-\frac{2z}{5}\right)\\ &=\text{Rs.}\ \frac{3z}{5}\\ &\therefore\mathrm{X}:\mathrm{Y}&\\ &=\frac{3z}{5}:\frac{2z}{5}&\\ &=3:2&\end{aligned}$ Let the total capital be Rs. x and Suppose Y’s money was used for y months Then, $\begin{array}{l} \Rightarrow \Large\frac{\frac{1}{3} x \times 9}{\frac{2}{3} x \times y}=\frac{3}{2} \\ \Rightarrow 18 x=6 x y \\ \Rightarrow y=3 \end{array}$ Hence, Y’s money was used for 3 months.

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