Question

A, B and C can do a piece of work 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 the work
Remaining work = ${(1-\frac{5}{12})}^{th}=\frac{7^{th}}{12}$ part
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
= $\frac{1}{7/24}\times \frac{7}{12}=\frac{24}{7}\times \frac{7}{12}=2$ days