A can do a work in 8 days , B can do the same work in 10 days and C can do the same work in 12 days . If all three of them do the same work together and they are paid Rs. 7400, what is the share (in Rs.) of B ?

Options

A. 2600
B. 3000
C. 2400
D. 2000

Answer

To solve the problem step by step, we will first determine the work done by each person in one day, then calculate their shares based on the ratio of work done, and finally find B's share of the total payment.

### Step-by-Step Solution:

1. **Determine the work done by A, B, and C in one day:**
- A can complete the work in 8 days, so A's work in one day = \( \frac{1}{8} \).
- B can complete the work in 10 days, so B's work in one day = \( \frac{1}{10} \).
- C can complete the work in 12 days, so C's work in one day = \( \frac{1}{12} \).

2. **Find the LCM of the denominators (8, 10, and 12):**
- The LCM of 8, 10, and 12 is 120.

3. **Convert the work done in one day into a common ratio:**
- A's work in one day = \( \frac{120}{8} = 15 \)
- B's work in one day = \( \frac{120}{10} = 12 \)
- C's work in one day = \( \frac{120}{12} = 10 \)

4. **Establish the ratio of work done by A, B, and C:**
- The ratio of work done by A, B, and C is 15:12:10.

5. **Calculate the total parts in the ratio:**
- Total parts = \( 15 + 12 + 10 = 37 \).

6. **Determine B's share of the total payment:**
- B's share in the ratio = 12 parts.
- Total payment = Rs. 7400.
- B's share = \( \frac{12}{37} \times 7400 \).

7. **Calculate B's share:**
- B's share = \( \frac{12 \times 7400}{37} = \frac{88800}{37} \approx 2400 \).

### Final Answer:
B's share of the payment is Rs. 2400.