A takes 6 days less than B to finish a piece of work. If both A and B

together can finish the work in 4 days, find the time taken by B to

finish the work.

Asked by Topperlearning User | 7th Nov, 2013, 03:55: AM

Expert Answer:

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 =

Therefore,

8x - 24 = x2 - 6x

x2 - 14x + 24 = 0

x2 - 12x - 2x + 24 = 0

(x - 12) (x - 2) = 0

x = 12 or x = 2

But, x cannot be less than 6. So, x = 12.

Hence, B alone can finish the work in 12 days.

Answered by  | 7th Nov, 2013, 05:55: AM