###
**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**

## Show Answer

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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