Question

A and B invested some money in a business in the ratio 3 : 2, but A withdrew his money after a few months. If, at the end 18 months, profit was shared by A and B in the ratio 1 : 1, for many months did A invested in the business?
1. 8 months
2. 10 months
3. 15 months
4. 12 months

Answer 1

Correct Answer - Option 4 : 12 months

Given:

Ratio of capital invested = 3 ∶ 2

Ratio of profit shared = 1 ∶ 1

Concept:

The ratio of profit is shared in the ratio of capital invested for the given time.

Calculation:

∵ The profit is equally divided.

Let the capital of A and B = 3a and 2a

Time of investment of A = 'b' months

∴ 3a × b = 2a × 18 months 

⇒ b = (2a × 18)/3a

⇒ b = 12 months