Question

$A$ can do $\frac{1}{2}$ of a piece of work in 5 days, $B$ can do $\frac{3}{5}$ of the same work in 9 days and $C$ can do $\frac{2}{3}$ of that work in 8 days. In how many days can the three of them together do the work ?

Answer 1

$A$ can do $\frac{1}{2}$ of the work in 5 days $\Rightarrow A$ can do the whole work in $5\times \frac{2}{1}=10$ days
$B$ can do $\frac{3}{5}$ of the work in 9 days $\Rightarrow B$ can do the whole work in $9\times \frac{5}{3}=15$ days
$C$ can do $\frac{2}{3}$ of that work in 8 days $\Rightarrow C$ can do the whole work in $8\times \frac{3}{2}$ days $=12$ days
$\therefore (A+B+C)$'s 1 days' work $=\frac{1}{10}+\frac{1}{15}+\frac{1}{12}=\frac{6+4+5}{60}=\frac{15}{60}=\frac{1}{4}$
Hence, $A+B+C$ can complete the whole work in 4 days.