Question

$A$ and $B$ can do a piece of work in $18$ days. $B$ and $C$ can do it in $24$ days while $C$ and $A$ can finish it in $36$ days. In how many days can $A,B,C$ finish it. if they all work together?

Answer 1

Given: $A$ and $B$'s one day's work $=\frac{1}{18}$.....(i)

$B$ and $C$'s one day's work $=\frac{1}{24}$.....(ii)

$C$ and $A$'s one days work $=\frac{1}{36}$......(iii)
Adding above three equations, we get
$2(A+B+C)$'s one day's work $=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}$

$=\frac{4+3+2}{72}$ {LCM $18,24$ and $36=72$}
$=\frac{9}{72}$
$\therefore 2(A+B+C)$'s one day's work $=\frac{1}{8}$

Hence, $A,B$ and $C$'s one day work $=\frac{1}{8\times 2}=\frac{1}{16}$

$\therefore$ $A,B$and $C$ can do the work in $16$ days.