Question

$A$ and $B$ together can do a piece of work in $8$ days, but $A$ alone can do it in $12$ days. How many days would $B$ alone take to do the same work?

Answer 1

Work done by $A$ and $B$ together in $1$ day $=\frac{1}{8}$ of the work
Work done by $A$ in $1$ day $=\frac{1}{12}$ of the work

Work done by $B$ in $1$ day $=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$

Number of days taken by $B$ alone to do the same work

$=\frac{1}{\frac{1}{24}}=24days$