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1. Rahul, Arun and Sumit started a business. Rahul invested $\frac{1}{2}$ part, Arun $\frac{1}{3}$ part and rest of the capital was invested by Sumit. The ratio of their profits will be = ?

A. 2 : 3 : 1

B. 3 : 2 : 1

C. 2 : 3 : 6

D. 3 : 2 : 5

Solution:

Let total capital be Rs. x

\begin{aligned} Then, \\ Rahul's share \\ = Rs . \frac{x}{2} \\ Arun's share = Rs . \frac{x}{3} \\ Sumit's share \\ = Rs . [x - (\frac{x}{2} + \frac{x}{3})] \\ = Rs . \frac{x}{6} \\ ∴ Required ratio \\ = \frac{x}{2} : \frac{x}{3} : \frac{x}{6} \\ = \frac{1}{2} : \frac{1}{3} : \frac{1}{6} \\ = 3 : 2 : 1 \end{aligned}

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