Question

Three friends A, B and C started a business by investing in the ratio of 1/2 ∶ 1/3 ∶ 1/4. At the end of the year, they earned a profit of Rs. 10,400, which is 10% of the total investment. How much did B invest?
1. Rs. 32,000
2. Rs. 36,000
3. Rs. 30,000
4. Rs. 35,000

Answer 1

Correct Answer - Option 1 : Rs. 32,000

Given:

Ratio of investments of A, B and C = 1/2 ∶ 1/3 ∶ 1/4

Total profit at the end of the year = Rs. 10400

Total profit = 10% of the total investment

Concept used:

Ratio of product of time and investment = Ratio of profit

When the investments made by all partners are for the same time period, then profit is distributed amongst them in the ratio of their investments

Calculation:

Ratio of investments = 1/2 ∶ 1/3 ∶ 1/4 = 6 ∶ 4 ∶ 3

Let, investments of A, B and C are 6X, 4X and 3X respectively, therefore total investment = 13X

Ratio of profit = 6 ∶ 4 ∶ 3 (Using concept)

Total profit = 10400 = 10% of 13X (Given)

⇒ 10% of 13X = 10400

⇒  X = 10400/13 × 10 = 8000

∴  Investment of B = 4X = 4 × 8000 = Rs. 32000