Rahul and Bharti are partners in a business. Rahul contributes $\frac{1}{4} \text { th }$ capital for 15 months and Bharti received $\frac{2}{3}$ of profit. For how long Bharti money was used.

A. 8 months B. 10 months C. 11 months D. 17 months Answer: Option B
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Solution(By Apex Team)

$\begin{array}{l}\text{ Let the total profit be }Rs.Z\\ \begin{aligned}\text{ Bharti’s share }&=\frac{2}{3}Z\\ \text{ Rahul’s share }&=Z-\frac{2}{3}Z\\ &=\frac{Z}{3}\end{aligned}\end{array}$ $\begin{aligned}&\text{ Rahul:Bharti }\\ &=\frac{Z}{3}:\frac{2}{3}Z=1:2\end{aligned}$ $\begin{aligned}&\text{Now let the total capital be Rs X,}\\ &\text{and Bharti capital was used for Y months.}\\ &\text{then, Rahul capital will be}\ \frac{1}{4}X\\ &\text{and Bharati CApital will be}\ \left(X-\frac{1}{4}X\right)\\ &=\frac{3X}{4}\\ &\Rightarrow\frac{\frac{1}{4}X\times15}{\frac{3}{4}X\times Y}=\frac{1}{2}\\ &\therefore\text{Y}=\frac{15\times2}{3}=10\end{aligned}$ So, Bharati’s money was used for 10 months

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