Question

Anil started a business with Rs. 2,500 and was joined by Virat with Rs. 4,000. If the profit at the end of the year was divided in the ratio of 3 ∶ 2, after how much time Virat joined the business?
1. 9 months
2. 8 months
3. 7 months
4. 6 months

Answer 1

Correct Answer - Option 3 : 7 months

Given:

Investment of Anil = Rs. 2500 for 12 months

Investment of Virat = Rs. 4000

Ratio of profit at the end of year = 3 ∶ 2

Concept used:

Ratio of product of time and investment = Ratio of profit

Calculation:

Let, Virat joined after t months

Investment of Anil for 1 year = Rs. 2500 for 12 months = Rs. (2500 × 12) = Rs. 30000

Investment of Virat for 1 year = Rs. 4000 for T months = Rs. 4000T, where T = (12 – t)

Ratio of product of time and investment = Ratio of profit

Ratio of profit = 30000 ∶ 4000T = 15 ∶ 2T = 3 ∶ 2 (Given)

Equating two ratios, 15/2T = 3/2

⇒ T = 15/3 = 5

⇒ t = 12 – 5 = 7

∴ Virat joined after 7 months.