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
Answer
Answer (as printed): B
Explanation
Let the total capital be ₹ $x$. Then, Rahul's share $=₹ \frac{x}{2}$, Arun's share $=₹ \frac{x}{3}$. Sumit's share $=₹\left[x-\left(\frac{x}{2}+\frac{x}{3}\right)\right]=₹ \frac{x}{6}$. ∴ Required ratio $=\frac{x}{2}: \frac{x}{3}: \frac{x}{6}=\frac{1}{2}: \frac{1}{3}: \frac{1}{6}=3: 2: 1$.
Explanation as extracted from the printed page; notation may be imperfect.