Question

A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got Rs. 94.60 in all. When they divide the money among themselves, A, B and C will respectively get (in Rs.):

• A. 44, 33, 17.60
• B. 43, 27.20, 24.40
• C. 45, 30, 19.60
• D. 42, 28, 24.60

Hint:

When total payment is to be split by work done, calculate work rate ratios, sum the parts, and multiply by per-part value.

Answer 1

The Correct Option is A

Work rates:
A: $\frac{1}{6}$ work/hour, B: $\frac{1}{8}$ work/hour, C: $\frac{1}{15}$ work/hour.
Total rate = $\frac{1}{6} + \frac{1}{8} + \frac{1}{15} = \frac{20 + 15 + 8}{120} = \frac{43}{120}$ work/hour.
Shares are proportional to rates:
A:B:C = $\frac{1}{6} : \frac{1}{8} : \frac{1}{15}$ = LCM(120) form → $20 : 15 : 8$.
Sum of ratio parts = $20 + 15 + 8 = 43$. Total payment Rs. 94.60, so each part = Rs. $94.60 / 43 = Rs. 2.20$.
Thus: A’s share = $20 \times 2.20 = Rs. 44.00$
B’s share = $15 \times 2.20 = Rs. 33.00$
C’s share = $8 \times 2.20 = Rs. 17.60$