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 B alone takes x days to finish the work. Then, B’s one day’s work = `1/x`.

Similarly, A alone can finish it in (x - 10) days to finish the work. Then, A’s one day’s work `=1/(x-10)`.

It is given that

A’s one day’s work + B’s one day’s work = (A + B)’s one day’s work

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

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

`(2x-10)/(x^2-10x)=1/12`

x² - 10x = 12(2x - 10)

x² - 10x = 24x - 120

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

x = 30

Or

x - 4 = 0

x = 4

But x = 4 is not correct.

Therefore, x = 30 is correct.

Hence, the time taken by B to finish the work is x = 30 days.