A' complete 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 ?

Question

Accepted Answer

To determine how much amount 'B' gets when A, B, and C work together on a job and earn Rs. 3900, we need to calculate the share of the payment based on their individual work rates.

1. **Calculate Individual Work Rates:**
   - 'A' completes the job in 2 days, so A's work rate is $ \frac{1}{2} $ of the job per day.
   - 'B' completes the job in 3 days, so B's work rate is $ \frac{1}{3} $ of the job per day.
   - 'C' completes the job in 4 days, so C's work rate is $ \frac{1}{4} $ of the job per day.

2. **Calculate Combined Work Rate:**
   - Combined work rate of A, B, and C = $ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} $.
   - To add these fractions, find a common denominator, which is 12.
   - Convert each fraction: $ \frac{1}{2} = \frac{6}{12} $, $ \frac{1}{3} = \frac{4}{12} $, $ \frac{1}{4} = \frac{3}{12} $.
   - Combined work rate = $ \frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12} $.

3. **Calculate Individual Contributions:**
   - Total work done by A, B, and C together is 1 job.
   - Contribution of 'B' = B's work rate / Combined work rate = $ \frac{1/3}{13/12} = \frac{1}{3} \times \frac{12}{13} = \frac{4}{13} $.

4. **Calculate B's Share of the Payment:**
   - Total payment = Rs. 3900.
   - B's share = $ \frac{4}{13} \times 3900 = 1200 $.

Therefore, 'B' gets Rs. 1200, which corresponds to Option 2.

**Explanation of Incorrect Options:**

- **Option 1 (Rs. 1800):** This option suggests that B's contribution is higher than calculated. Given B's work rate and the combined work rate, Rs. 1800 would imply a larger share than B's actual contribution of $ \frac{4}{13} $.

- **Option 3 (Rs. 900):** This option underestimates B's contribution. B's calculated share is $ \frac{4}{13} $ of the total payment, which is Rs. 1200, not Rs. 900.

- **Option 4 (Rs. 800):** Similar to Option 3, this option significantly underestimates B's contribution. The calculation clearly shows B's share is Rs. 1200.

Thus, the correct answer is Option 2, Rs. 1200, based on the logical and factual calculations provided.