Question

A and B can finish a work in 10 days and 15 days respectively. They together work on it for 5 days and then the rest of the work is finished by C in 2 days. They get INR 450 for finishing this work. What should be the shares of A, B, and C respectively?

• A. A = INR 180, B = INR 120, C = INR 150
• B. A = INR 225, B = INR 120, C = INR 105
• C. A = INR 225, B = INR 150, C = INR 75
• D. None of these

Hint:

When dividing the total payment based on the work done, divide the total work based on the rates of work of each individual and allocate the payment accordingly.

Answer 1

The Correct Option is C

Let the total work be \( W \).
A’s rate of work = \( \frac{1}{10} \) work/day,
B’s rate of work = \( \frac{1}{15} \) work/day.
Together A and B work for 5 days, so the work done by A and B is:
\[ \text{Work done by A and B in 5 days} = 5 \times \left( \frac{1}{10} + \frac{1}{15} \right) \] \[ = 5 \times \left( \frac{3}{30} + \frac{2}{30} \right) = 5 \times \frac{5}{30} = \frac{25}{30} = \frac{5}{6} \] So, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{5}{6} = \frac{1}{6} \] C finishes the remaining work in 2 days, so C’s rate of work is:
\[ \text{C’s rate of work} = \frac{1}{6} \div 2 = \frac{1}{12} \text{ work/day} \] Now, we divide the INR 450 according to their work contributions:
- A’s contribution in 5 days = \( 5 \times \frac{1}{10} = \frac{5}{10} = \frac{1}{2} \),
- B’s contribution in 5 days = \( 5 \times \frac{1}{15} = \frac{5}{15} = \frac{1}{3} \),
- C’s contribution in 2 days = \( 2 \times \frac{1}{12} = \frac{2}{12} = \frac{1}{6} \).
Total work = \( 1 \).
Therefore, the share of each person:
- A’s share = \( \frac{1}{2} \times 450 = 225 \),
- B’s share = \( \frac{1}{3} \times 450 = 150 \),
- C’s share = \( \frac{1}{6} \times 450 = 75 \). Answer: A gets INR 225, B gets INR 150, and C gets INR 75.