Question

A, B and C can do a piece of work in 4, 5 and 7 days respectively. If they get Rs.415 for working together to complete the job, then A's share is

• A. 170
• B. 185
• C. 175
• D. 180

Hint:

To find the share of an individual when multiple people work together, calculate the work rate of each person, find the total work rate, and then distribute the total earnings based on individual work rates.

Answer 1

The Correct Option is C

A's work rate is \( \frac{1}{4} \) of the work per day, B's work rate is \( \frac{1}{5} \), and C's work rate is \( \frac{1}{7} \). The total rate of work for A, B, and C working together is: \[ \frac{1}{4} + \frac{1}{5} + \frac{1}{7} = \frac{35 + 28 + 20}{140} = \frac{83}{140}. \] Thus, the total work is completed in \( \frac{140}{83} \) days. A's share of the total work is \( \frac{1}{4} \times \frac{140}{83} \). So A's share of Rs.415 is: \[ \text{A's share} = \frac{1}{4} \times 415 = 175. \]