Question

$A$, $B$ and $C$ can separately do a work in $2$, $6$ and $3$ days respectively. Working together, how much time would they require to do it? If the work earns them $₹960$, how should they divide the money?

Answer 1

Given,

$A$, $B$ and $C$ can separately do a work in $2$, $6$ and $3$ days

Thus,

$A$’s one day work = $\frac{1}{2}$

$B$’s one day work = $\frac{1}{6}$

$C$’s one day work = $\frac{1}{3}$

Work done by $A+B+C$ in one day when working together $=\frac{1}{2}+\frac{1}{6}+\frac{1}{3}$

$=\frac{3+1+2}{6}=\frac{6}{6}=1$

$\therefore$ $A$, $B$ and $C$ can finish the work by working together in $1$ day.

So they should divide the money in the ratio $\frac{1}{2}:\frac{1}{6}:\frac{1}{3}$

So, sum of terms of ratio $=\frac{1}{2}+\frac{1}{6}+\frac{1}{3}=\frac{3+1+2}{6}=\frac{6}{6}=1$

$\therefore$ $A$’s share = $\frac{1}{2}\times ₹960=₹480$

$B$’s share $=\frac{1}{6}\times ₹960=₹160$

$C$’s share $=\frac{1}{3}\times ₹960=₹320$