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**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**

## Show Answer

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.

## Related Questions On Partnership

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D. None of these

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