Question

A takes $6$ days less than $B$ to do work. If both $A$ and $B$ working together can do it in $4$ days, how many days will $B$ take to finish it?

Answer 1

Suppose B alone takes $x$ days to finish the work. Then, A alone can finish it in $(x-6)$ days.

Now,
A's one day's work + B's one day's work = (A + B)'s one day's work
$\Rightarrow \frac{1}{x}+\frac{1}{x-6}=\frac{1}{4}$

or, $\frac{2x-6}{x(x-6)}=\frac{1}{4}$

or, $8x-24=x^2-6x$

or, $x^2-14x+24=0$

or, $(x-12)(x-2)=0$

$x=2,12$.

But $x=12$ is acceptable otherwise A's day to finish the work will be meaning-less.

So B takes $12$ days to finish the work.