Question

A man and a boy working together can complete a work in 24 days, if for the last 6 days, the man alone does the work, then it is completed in 26 days, How long will the boy to complete the work alone ?

• A. 72 Days
• B. 20 Days
• C. 24 Days
• D. 36 Days

Answer 1

The correct option is A 72 Days

Let 1 man's 1 days' work = $\frac{1}{x}$ and 1 boy's 1 days' work = $\frac{1}{y}$ Then $\frac{1}{x}+\frac{1}{y}=\frac{1}{24}$
Also given $\frac{20}{x}+\frac{20}{y}+\frac{6}{x}=1$ $\Rightarrow$ $20(\frac{1}{x}+\frac{1}{y})+\frac{6}{x}=1\Rightarrow 20\left(\frac{1}{24}\right)+\frac{6}{x}=1$
$\Rightarrow \frac{6}{x}=1-\frac{5}{6}\Rightarrow \frac{6}{x}=\frac{1}{6}\Rightarrow x=36$ $\therefore$ $\frac{1}{y}=\frac{1}{24}-\frac{1}{36}=\frac{3-2}{72}=\frac{1}{72}\Rightarrow y=72$
$\therefore$ The boy will take 72 days to complete the work alone