Question

A,B and C can complete a work in $6,12$, and $18$ days respectively. A and B started the work and C joined them after one day.B left $2$ days before the work complete.Find number of days they all work together.

Answer 1

Let the Work to be done be $W$

Work Done per day by

$A:\frac{W}{6}B:\frac{W}{12}C:\frac{W}{18}$

Let us assume that they work together for $x$ days

So,

$1(\frac{W}{6}+\frac{W}{12})+x(\frac{W}{6}+\frac{W}{12}+\frac{W}{18})+2(\frac{W}{6}+\frac{W}{18})=W\Rightarrow \frac{11Wx+25W}{36}=W\Rightarrow \frac{11x+25}{36}=1\Rightarrow 11x=11\Rightarrow x=1$