Question

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.

Options

• 12 days

• `12 1/2` days

• 13 days 

• 15 days

Answer 1

12 days

Explanation:

Assuming that 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 = `1/"x" + 1/("x" − 6)`

and (A+B)’s one day’s work = `1/4`

`("x" - 6)/("x"("x" - 6)) + "x"/("x"("x" - 6)) = 1/4`

4(x − 6 + x) = x² − 6x

4(2x − 6) = x² − 6x

8x − 24 = x² − 6x

0 = x² − 14x + 24

0 = (x − 12) (x − 2)

x = 12 and 2

x cannot be less than 6.

So x = 12 Therefore, B also can finish the work in 12 days.