Question

$A$ and $B$ working together can finish a piece of work in $6$ days, while $A$ alone can do it in $9$ days. How much time will $B$ alone take to finish it?

Answer 1

We know that,
Number of days $A$ required to do a piece of work $=9$ days
Let us consider number of days $B$ required to do piece of work $=X$ days
Number of days required by $A$ and $B$ together to do a piece of work $=6$ days
$\therefore$ We can calculate, work done by $A$ in $1$ day $=1/9$
And the work done by $B$ in $1$ day $=1/x$
Work done by both $A$ and $B$ in a day $=1/6$
Work done by both $A$ and $B$ together in $1$ day $=1/9+1/x=(x+9)/9x$

$\Rightarrow (x+9)/9x=1/6$

$\Rightarrow 6x+54=9x$

$\Rightarrow 3x=54$

$\Rightarrow x=54/3$

$\Rightarrow x=18$

$\therefore B$ can do the work in $18$ days