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1. Rahul and Bharti are partners in a business. Rahul contributes $\frac{1}{4}$ 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

Solution:

\begin{aligned} Let the total profit be R s . Z \\ Bharti's share = \frac{2}{3} Z \\ Rahul's share = Z - \frac{2}{3} Z \\ = \frac{Z}{3} \\ Rahul:Bharti \\ = \frac{Z}{3} : \frac{2}{3} Z = 1 : 2 \\ Now let the total capital be R s X, \\ and Bharti capital was used for Y months . \\ then, Rahul capital will be \frac{1}{4} X \\ and Bharti capital will be X - \frac{1}{4} X \\ = \frac{3 X}{4} \\ \frac{\frac{1}{4} X * 15}{\frac{3}{4} X * Y} = \frac{1}{2} \\ Y = \frac{15 * 2}{3} = 10 \\ So, Bharti's money was used for 10 months \end{aligned}

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