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Rahul, Arun and Sumit started a business. Rahul invested $\Large\frac{1}{2}$ part, Arun $\Large\frac{1}{3}$ 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 Answer: Option B
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Solution(By Apex Team)

Let total capital be Rs. x $\begin{aligned}&\text{Then,}\\ &\text{Rahul’s share}\\ &=\text{Rs.}\ \frac{x}{2}\\ &\text{Arun’s share}\\ &=\text{Rs.}\ \frac{x}{3}\\ &\text{Sumit’s share}\\ &=\text{Rs.}\ \left[x-\left(\frac{x}{2}+\frac{x}{3}\right)\right]\\ &=\text{Rs.}\ \frac{x}{6}\\ &\therefore\text{Required ratio}\\ &=\frac{x}{2}\ :\ \frac{x}{3}\ :\ \frac{x}{6}\\ &=\frac{1}{2}\ :\ \frac{1}{3}\ :\ \frac{1}{6}\\ &=3\ :\ 2\ :\ 1\end{aligned}$

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