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

1.	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 ? (a) Rs 375 (b) Rs 400 (c) Rs 600 (d) Rs 800
Answer» (b) Rs 400 Let C does the same work in x days. Then, \(3\big(\frac{1}{6}+\frac{1}{8}+\frac{1}{X}\big)\) = 1 \(\Rightarrow\) \(\frac{7}{24}\) + \(\frac{1}{X}\) = \(\frac{1}{3}\) \(\Rightarrow\) \(\frac{1}{X}\)= \(\frac{1}{3}\)- \(\frac{7}{24}\) = \(\frac{1}{24}\) \(\therefore\) C will do the same work in 24 days. The ratio of their one days’ work = \(\frac{1}{6}:\frac{1}{8}:\frac{1}{24}\) = 4 : 3 : 1 The amount to be paid to C = \(\frac{1}{(4+3+1)}\)x Rs 3200 = Rs 400.

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 ? (a) Rs 375 (b) Rs 400 (c) Rs 600 (d) Rs 800

Answer»

(b) Rs 400

Let C does the same work in x days. Then,

\(3\big(\frac{1}{6}+\frac{1}{8}+\frac{1}{X}\big)\) = 1 \(\Rightarrow\) \(\frac{7}{24}\) + \(\frac{1}{X}\) = \(\frac{1}{3}\)

\(\Rightarrow\) \(\frac{1}{X}\)= \(\frac{1}{3}\)- \(\frac{7}{24}\) = \(\frac{1}{24}\)

\(\therefore\) C will do the same work in 24 days.

The ratio of their one days’ work = \(\frac{1}{6}:\frac{1}{8}:\frac{1}{24}\) = 4 : 3 : 1

The amount to be paid to C

= \(\frac{1}{(4+3+1)}\)x Rs 3200 = Rs 400.