A' completes a job in 2 days and 'B' completes it in 3 days and 'C' completes it in 4 days. If they work together and get Rs. 3900 for the job, then how much amount does 'B' get'?

Options

A. Rs. 1800
B. Rs. 1200
C. Rs. 900
D. Rs. 800

Answer

To find out how much amount 'B' gets when 'A', 'B', and 'C' work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- 'A' completes the job in 2 days, so in one day, 'A' does \( \frac{1}{2} \) of the work.
- 'B' completes the job in 3 days, so in one day, 'B' does \( \frac{1}{3} \) of the work.
- 'C' completes the job in 4 days, so in one day, 'C' does \( \frac{1}{4} \) of the work.

### Step 2: Calculate the total work done by 'A', 'B', and 'C' in one day.
- Total work done in one day by 'A', 'B', and 'C' together is:
\[ \text{Total work} = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 2, 3, and 4 is 12. Therefore, we convert each fraction:
\[ \frac{1}{2} = \frac{6}{12}, \quad \frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12} \]
- Now, adding them together:
\[ \text{Total work} = \frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12} \]

### Step 3: Calculate the share of work done by 'B'.
- The share of work done by 'B' in one day is \( \frac{1}{3} \).
- To find the fraction of the total work done by 'B', we calculate:
\[ \text{B's share} = \frac{\text{B's work}}{\text{Total work}} = \frac{\frac{1}{3}}{\frac{13}{12}} = \frac{1}{3} \times \frac{12}{13} = \frac{12}{39} = \frac{4}{13} \]

### Step 4: Calculate the amount 'B' receives from the total payment.
- The total payment for the job is Rs. 3900.
- 'B's share of the payment is:
\[ \text{B's amount} = \text{Total payment} \times \text{B's share} = 3900 \times \frac{4}{13} \]
- Calculating this gives:
\[ \text{B's amount} = 3900 \times \frac{4}{13} = 3900 \div 13 \times 4 = 300 \times 4 = 1200 \]

### Final Answer:
Thus, 'B' gets Rs. 1200.

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