A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, how many days will B take to finish the work?

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

1/x + 1/x−6 = 1/4

x-6+x/x(x-6) = 1/4 = 2x-6/x 2 -6x = 1/4 =

8x−24=x2−6x ⇒x2−14x+24=0

⇒x2−12x−2x+24 = 0

⇒(x−12) (x−2) = 0

⇒x=12 or x = 2 x cannot be less than 6.

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

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