Question

$A,B$ and $C$ can do a piece of work in $6,8$ and $12$ days respectively. $B$ and $C$ work together for $2$ days, then $A$ takes $C$'s place. How long will it take to finish the work?

Answer 1

Work done by B & C in 2 days = $2\times \{\frac{1}{8}+\frac{1}{12}\}$
= $\frac{5^{th}}{12}$ part of thw work
Remaining work = ${(1-\frac{5}{12})}^{th}=\frac{7^{th}}{12}$ park
A and B's one day work = ${(\frac{1}{6}+\frac{1}{8})}^{th}={\left(\frac{7}{24}\right)}^{th}$ part
So $\frac{7^{th}}{24}$ part of work is completed in 1 day

$\therefore$ $\frac{7^{th}}{12}$ part of work will be completed in

= $\frac{1}{\frac{7}{24}}\times \frac{7}{12}=2$ days