A and B start a business jointly. A invests Rs. 16,000 for 8 months and remains B in the business for 4 months. Out of total profit, B claims `2/7` of the profit. How much money was contributed by B ?

Options

A. Rs. 10,500
B. Rs. 11,900
C. Rs. 12,800
D. Rs. 13,600

Answer

To solve the problem, we need to determine how much money B contributed to the business based on the information provided. Here's a step-by-step solution:

### Step 1: Calculate A's Investment Contribution
A invests Rs. 16,000 for 8 months. The contribution of A in terms of capital months is calculated as follows:

\[ \text{A's Contribution} = \text{Capital} \times \text{Time} = 16000 \times 8 = 128000 \text{ capital months} \]

### Step 2: Set Up the Equation for B's Contribution
Let B's investment be Rs. X. Since B invests for 4 months, the contribution of B in terms of capital months is:

\[ \text{B's Contribution} = X \times 4 \]

### Step 3: Determine the Profit Sharing Ratio
According to the problem, B claims \( \frac{2}{7} \) of the total profit. Therefore, A's share of the profit will be:

\[ \text{A's Share} = 1 - \frac{2}{7} = \frac{5}{7} \]

### Step 4: Set Up the Ratio of Contributions
The ratio of A's and B's contributions can be equated to their shares of the profit:

\[ \frac{\text{A's Contribution}}{\text{B's Contribution}} = \frac{\text{A's Share}}{\text{B's Share}} \]

Substituting the values we have:

\[ \frac{128000}{X \times 4} = \frac{5/7}{2/7} \]

### Step 5: Simplify the Right Side
The right side simplifies as follows:

\[ \frac{5/7}{2/7} = \frac{5}{2} \]

### Step 6: Set Up the Equation
Now we have:

\[ \frac{128000}{X \times 4} = \frac{5}{2} \]

Cross-multiplying gives:

\[ 128000 \times 2 = 5 \times (X \times 4) \]

This simplifies to:

\[ 256000 = 20X \]

### Step 7: Solve for X
Now, divide both sides by 20 to find X:

\[ X = \frac{256000}{20} = 12800 \]

### Conclusion
B contributed Rs. 12,800 to the business.