Discussion
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answer: B
Work in rates: someone who finishes a job in \( n \) days does \( \tfrac{1}{n} \) of it a day, and rates add.
All three together finish in 3 days, so their combined rate is \( \tfrac{1}{3} \).
\[ \frac{1}{6} + \frac{1}{8} = \frac{4 + 3}{24} = \frac{7}{24} \]
\[ C = \frac{1}{3} - \frac{7}{24} = \frac{8 - 7}{24} = \frac{1}{24} \]
C's share of the work is \( \tfrac{1/24}{1/3} = \tfrac{1}{8} \):
\[ \frac{3200}{8} = \text{Rs. } 400 \]
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