Question

$A$ and $B$ can finish a piece of work in $16$ days and $12$ days respectively. A started the work and worked at it for $2$ days. He was then joined by B. Find the total time taken to finish the work.

Answer 1

Let whole work be $W.$

$\Rightarrow$ Work done by $A$ in one day $=\frac{W}{16}$

Work is done by $B$ in one day $=\frac{W}{12}$

$\Rightarrow$ A worked for $2$ days $=2\times \frac{W}{16}$

$=\frac{W}{8}$

$A$ and $B$ worked for $x$ days ( let )

$\Rightarrow \frac{W}{8}+x(\frac{W}{16}+\frac{W}{12})=W$

$\Rightarrow x\times \frac{7}{48}=\frac{7}{8}$

$\Rightarrow x=6$ days.

Hence, the answer is $6$ days.