Question

A, B and C can finish a piece of work in 12, 15 and 20 days respectively. If all the three work at it together and they are paid ₹ 9,600 for the whole work, what is B’s share ?

• A. 4,000
• B. 3,200
• C. 2,400
• D. 2,700

Answer 1

The Correct Option is B

To determine B's share of the payment, we first need to figure out the work rates of A, B, and C, and then calculate their respective contributions to the total work.

1. Calculate the work rate for each person:

• A's work rate is \( \frac{1}{12} \) of the work per day since A completes the work in 12 days.
• B's work rate is \( \frac{1}{15} \) of the work per day since B completes the work in 15 days.
• C's work rate is \( \frac{1}{20} \) of the work per day since C completes the work in 20 days.

2. Determine the combined work rate of A, B, and C working together: \[ \text{Total work rate} = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} \] To add these fractions, find the least common multiple (LCM) of the denominators 12, 15, and 20, which is 60: \[ \frac{1}{12} = \frac{5}{60}, \quad \frac{1}{15} = \frac{4}{60}, \quad \frac{1}{20} = \frac{3}{60} \] \[ \text{Total work rate} = \frac{5}{60} + \frac{4}{60} + \frac{3}{60} = \frac{12}{60} = \frac{1}{5} \] Hence, A, B, and C together complete \( \frac{1}{5} \) of the work per day.

3. Calculate B's share of the work: Since the combined work rate is \( \frac{1}{5} \), this means they complete the work in 5 days. B's contribution over 5 days is: \[ \text{B's contribution} = 5 \times \frac{1}{15} = \frac{5}{15} = \frac{1}{3} \] Therefore, B completes \( \frac{1}{3} \) of the total work when all three are working together.

4. Determine B's share of the payment: Since B completes \( \frac{1}{3} \) of the work, B's share of the ₹9,600 payment is: \[ \text{B's share} = \frac{1}{3} \times 9600 = 3200 \]

Thus, B's share of the payment is ₹3,200.