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

SOLUTION :  

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)

A.T.Q

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

[By middle term splitting]

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 is 30 days.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

hope this helps......