Discussion
A and B undertake a piece of work for Rs. 1200. A alone can do it in 15 days and B alone in 12 days. With the help of C they finish it in 5 days. What is C’s share of the wage?
Answer: B
Correct answer: Rs. 300
Wages divide in the ratio of work actually done, which for a common period is the ratio of the daily rates.
All three together complete the job in 5 days, so their combined rate is \(\tfrac{1}{5}\). Subtracting A and B gives C’s rate:
\[\frac{1}{5} - \frac{1}{15} - \frac{1}{12} = \frac{12}{60} - \frac{4}{60} - \frac{5}{60} = \frac{3}{60} = \frac{1}{20}\]
So the rates are \(\tfrac{1}{15} : \tfrac{1}{12} : \tfrac{1}{20}\), which on multiplying by 60 becomes \(4 : 5 : 3\).
\[\text{C’s share} = \frac{3}{4+5+3} \times 1200 = \frac{3}{12} \times 1200 = 300\]
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