Question

Anuj, Bheem, and Charles started a business by putting amounts in the ratio of 2:4:5. After six months, Anuj withdrew \( \frac{1}{4} \) of his capital. Bheem withdrew \( \frac{1}{4} \) of his initial capital after every quarter. Charles added \( \frac{2}{5} \) of his initial capital after every quarter. If the annual profit was Rs. 98000, what was the share of Bheem?

• A. Rs. 14000
• B. Rs. 18000
• C. Rs. 20000
• D. Rs. 21000
• E. Rs. 24000

Hint:

When solving profit-sharing problems, calculate the total contributions and then distribute the profit in the same ratio as the contributions.

Answer 1

The Correct Option is C

Step 1: Understanding the contributions of Anuj, Bheem, and Charles.
The ratio of the initial investments of Anuj, Bheem, and Charles is \( 2:4:5 \). After six months, the investments and withdrawals are considered as per the problem statement. 
Step 2: Contributions per quarter. 
\[ \text{Anuj's contribution for 1st quarter} = 2x, \quad \text{for 2nd quarter} = 2x, \quad \text{for 3rd quarter} = \frac{3}{4} \times 2x = 1.5x, \quad \text{for 4th quarter} = 1.5x \] \[ \text{Bheem's contribution for 1st quarter} = 4x, \quad \text{for 2nd quarter} = 3x, \quad \text{for 3rd quarter} = 2x, \quad \text{for 4th quarter} = x \] \[ \text{Charles' contribution for 1st quarter} = 5x, \quad \text{for 2nd quarter} = 7x, \quad \text{for 3rd quarter} = 9x, \quad \text{for 4th quarter} = 11x \] Step 3: Total contributions. 
The total contributions for the year (in terms of capital contributed each quarter) are: \[ \text{Anuj’s total contribution} = 2x + 2x + 1.5x + 1.5x = 7x \] \[ \text{Bheem’s total contribution} = 4x + 3x + 2x + x = 10x \] \[ \text{Charles’ total contribution} = 5x + 7x + 9x + 11x = 32x \] Step 4: Profit distribution. 
The total ratio of contributions is: \[ 7 : 10 : 32 \] The total profit is Rs. 98000. Bheem’s share will be proportional to his contribution. The total ratio is \( 7 + 10 + 32 = 49 \). Bheem’s share of the profit is: \[ \text{Bheem's share} = \frac{10}{49} \times 98000 = 20000 \] Final Answer: \[ \boxed{20000} \]