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?

• A. Rs. 400
• B. Rs. 800
• C. Rs. 1600
• D. None of these

Answer 1

Answer: (A)

Rs. 400

Sol.

Given,

A alone can do a piece of work in = 6 days

$\therefore$ A’s 1 day’s work = $\frac{1}{6}$

B alone can do a piece of work in = 8 days

$\therefore$ B’s 1 day’s work = $\frac{1}{8}$

Work done by A and B together in one day = $\frac{1}{6}$ + $\frac{1}{8}$

A, B and C together can do a piece of work in = 3 days

$\therefore$ 1 day’s work of A,B,C = $\frac{1}{3}$

$\therefore$ C’s 1 day’s work = $\frac{1}{3}–\left[\right(\frac{1}{6}+\frac{1}{8}$]

= $\frac{1}{3}-\frac{7}{24}$ = $\frac{1}{24}$
A’s wages : B’s wages : C’s wages =

$\frac{1}{6}$ : $\frac{1}{8}$ : $\frac{1}{24}$

= 4 : 3 : 1 ($\because$ LCM of 6,8,24=24)
So, C’s share for 3 days = Rs. (3 × $\frac{1}{24}\times 3200$) = Rs. 400