Tick $(\checkmark)$ the correct answer:
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
(a) $6 \frac{1}{2}$ days
(b) 7 days
(c) $7 \frac{1}{2}$ days
(d) 8 days
(c) $7 \frac{1}{2}$ daysA man can do a work in 5 days.
The man's 1 day work $=\frac{1}{5}$
The man and the son can do the work in 3 days.
The man and his son's 1 day work $=\frac{1}{3}$
Let the son's 1 day work be $\frac{1}{x}$.
Therefore,
$\frac{1}{3}=\frac{1}{5}+\frac{1}{x}$
or, $\frac{1}{x}=\frac{1}{3}-\frac{1}{5}=\frac{5-3}{15}=\frac{2}{15}$
$x=\frac{15}{2}=7 \frac{1}{2}$ days
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