Discussion
"A" can do a piece of work in 12 days. While "B" alone can do it in 15 days, with the help of "C" they can finish it in 5 days. If they are paid ₹ 960 for the whole work, what is the share of "A"?
Answer: C
A's share is ₹ 400.
Payment is shared in proportion to the work each does. In the 5 days the work takes, A does 5/12 of it and B does 5/15 = 1/3:
\[ \begin{aligned} C &= 1 - \tfrac{5}{12} - \tfrac{4}{12} = \tfrac{3}{12} \\ A &: B : C = 5 : 4 : 3 \end{aligned} \]
A's share is \(960 \times 5/12 = 400\), with B getting 320 and C 240. Sharing by the ratio of days (12 : 15) instead of work done gives the wrong amounts.
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