Rakesh, Amit, and Suresh started a business. Rakesh invested $$ \frac{1}{2} $$ part, Amit $$ \frac{1}{3} $$ part, and the rest of the capital was invested by Suresh. The ratio of their profits will be:

Question

Accepted Answer

The total capital is considered as $$ 1 $$.

- **Rakesh's Investment:** $$ \frac{1}{2} $$.  
- **Amit's Investment:** $$ \frac{1}{3} $$.  
- **Suresh's Investment:** The remaining part of the capital is:  
  $$
  Suresh's\ Part = 1 - \left( \frac{1}{2} + \frac{1}{3} ight)
  = 1 - \frac{5}{6} = \frac{1}{6}.
  $$

The ratio of their profits will be proportional to their investments. Hence, the ratio is given by:  
$$
	ext{Ratio of Profits} = \left( \frac{1}{2} : \frac{1}{3} : \frac{1}{6} ight) 	imes 6.
$$

Simplify the ratio:  
$$
\left( 3 : 2 : 1 ight).
$$

Thus, the ratio of their profits is **3:2:1**, which corresponds to option **(b)**.

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