In a business A and C Invested amounts in the ratio `2:1`, whereas A and B Invested amounts in the ratio 3:2. If their annual profit be Rs. 157300, then B's share in the profit is:

Options

A. Rs 24200
B. Rs 48000
C. Rs 3600
D. Rs 48000

Answer

To solve the problem, we need to find B's share in the profit based on the investment ratios given for A, B, and C.

### Step-by-Step Solution:

1. **Identify the Ratios**:
- A and C invested in the ratio of 2:1.
- A and B invested in the ratio of 3:2.

2. **Express Investments in Terms of A**:
- Let the investment of A be \(2x\) and C be \(x\) (from A and C's ratio).
- Let the investment of A be \(3y\) and B be \(2y\) (from A and B's ratio).

3. **Equate A's Investment**:
- From the two expressions for A's investment, we have:
\[ 2x = 3y \]
- Rearranging gives:
\[ y = \frac{2x}{3} \]

4. **Substitute y in B's Investment**:
- B's investment can be expressed as:
\[ B = 2y = 2 \left(\frac{2x}{3}\right) = \frac{4x}{3} \]

5. **Express C's Investment**:
- C's investment remains as:
\[ C = x \]

6. **Total Investment**:
- Now we can express the total investment in terms of \(x\):
\[ A + B + C = 2x + \frac{4x}{3} + x \]
- To combine these, we need a common denominator:
\[ = \frac{6x}{3} + \frac{4x}{3} + \frac{3x}{3} = \frac{13x}{3} \]

7. **Profit Distribution**:
- The total profit is given as Rs. 157300.
- The profit is distributed in the same ratio as the investments. The ratio of investments is:
\[ A : B : C = 2x : \frac{4x}{3} : x = 6 : 4 : 3 \]
- The total parts = \(6 + 4 + 3 = 13\).

8. **Calculate the Value of One Unit**:
- Since the total profit is Rs. 157300, we can find the value of one unit:
\[ 1 \text{ unit} = \frac{157300}{13} = 12100 \]

9. **Calculate B's Share**:
- B's share corresponds to 4 parts:
\[ B's \text{ share} = 4 \times 12100 = 48400 \]

### Final Answer:
B's share in the profit is Rs. 48400.