Question

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish. the work.

Answer 1

Let's B alone take x days to finish the work.
B’s 1 days work = $\frac{1}{x}$

A alone can finish the work in = x - 10
A’s 1 days work= $\frac{1}{x-10}$​​​​​​​

Given: A and B together can finish the same work in 12 days.
(A and B)'s 1 days work = $\frac{1}{12}$ ​​​​​​​

A’s 1 days work + B’s 1 days work = $\frac{1}{x}+\frac{}{}1x-10$​​​​​​​​​​​​​​

According to the question,

$12(2x-10)=x^2-10x$
$24x-120=x^2-10x$
$x^2-10x-24x+120=0$
$x^2-34x+120=0$
$x^{2}30x-4x+120=0$
$x(x-30)-4(x-30)=0$
$(x-30)(x-4)=0$
$(x-30)=0or(x-4)=0$

$x=30orx=4$
The value of x cannot be less than 10, so x= 30

Hence, the time taken by B to finish the work in 30 days