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 =
⇒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.