Question

Tick (✓) 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

Answer 1

(c) $7\frac{1}{2}days$

​$$\begin{gathered} \mathrm{A}\mathrm{man}\mathrm{can}\mathrm{do}\text{a}\mathrm{work}\mathrm{in}5\mathrm{days}. \\ \mathrm{The}\mathrm{man}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{5} \\ \mathrm{The}\mathrm{man}\mathrm{and}\mathrm{the}\mathrm{son}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{work}\mathrm{in}3\mathrm{days}. \\ \mathrm{The}\mathrm{man}\mathrm{and}\mathrm{his}\mathrm{son}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{3} \\ \mathrm{Let}\mathrm{the}\mathrm{son}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}\mathrm{be}\frac{1}{\mathrm{x}}. \\ \mathrm{Therefore}, \\ \frac{1}{3}=\frac{1}{5}+\frac{1}{\mathrm{x}} \\ \mathrm{or},\frac{1}{\mathrm{x}}=\frac{1}{3}-\frac{1}{5}=\frac{5-3}{15}=\frac{2}{15} \\ \mathrm{x}=\frac{15}{2}=7\frac{1}{2}\mathrm{days} \end{gathered}$$