A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertoo

Question

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?

Options:

A . Rs. 375

B . Rs. 400

C . Rs. 600

D . Rs. 800

Answer: Option B

C's 1 day's work = \(\frac{1}{3}-\left(\frac{1}{6}+\frac{1}{8}\right)=\frac{1}{3}-\frac{7}{24}=\frac{1}{24}.\)

A's wages : B's wages : C's wages = \(\frac{1}{6}:\frac{1}{8}:\frac{1}{24}=4:3:1.\)

So, C's share (for 3 days) = Rs. \(\left(3\times\frac{1}{24}\times3200\right)\) = Rs. 400.

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