Question

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

Answer 1

Answer:

Let's B alone take x days to finish the work.

B’s 1 days work = 1/x

A alone can finish the work in = x - 10

A’s 1 days work= 1/(x-10)

Given: A and B together can finish the same work in 12 days.

(A and B)'s 1 days work = 1/12

A’s 1 days work + B’s 1 days work = 1/x +  1/(x-10)

Therefore -

1/x +  1/(x-10) = 1/12

(x-10) + x / x(x-10) = 1/12

x-10  + x / x² -10x = 1/12

2x -10 / x² -10x = 1/12

12(2x -10) = x² -10x

24x -120 = x² -10x

x² -10x -24x +120= 0

x² -34x +120= 0

x² 30x -4x +120= 0

x( x -30) -4(x -30)= 0

(x-30)(x-4)= 0

(x-30) = 0  or  (x-4)= 0

x = 30  or  x= 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.