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1. In a partnership, A invests $\frac{1}{6}$ of the capital $\frac{1}{6}$ for of the time, B invests $\frac{1}{3}$ of the capital for $\frac{1}{3}$ of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, B's share is ?

A. Rs. 650

B. Rs. 800

C. Rs. 960

D. Rs. 1000

Solution:

\begin{aligned} Suppose, \\ A invests Rs . \frac{x}{6} for \frac{y}{6} months \\ Then, \\ B invests Rs . \frac{x}{3} for \frac{y}{3} months \\ C invests [x - (\frac{x}{6} + \frac{x}{3})] i . e ., Rs . \frac{x}{2} for y months \\ ∴ A : B : C \\ = (\frac{x}{6} \times \frac{y}{6}) : (\frac{x}{3} \times \frac{y}{3}) : (\frac{x}{2} \times y) \\ = \frac{1}{36} : \frac{1}{9} : \frac{1}{2} \\ = 1 : 4 : 18 \\ Hence, B's share \\ = Rs . (4600 \times \frac{4}{23}) \\ = Rs . 800 \end{aligned}

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