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 . Find the time taken by B to finish the work.

Explanation

Suppose B alone takes x days to finish the work and A alone can finish it in `(x-6)` days.
B's 1 day's work `=(1)/(x)`.
A's 1 day's work `=(1)/((x-6))`.
`(A+B)'s 1" day's work "=(1)/(4).`
`:." "(1)/(x)+(1)/((x-6))=(1)/(4)`
`implies" "((x-6)+x)/(x(x-6))=(1)/(4)implies((2x-6))/((x^(2)-6x))=(1)/(4)`
`implies" "x^(2)-6x=8x-24impliesx^(2)-14x+24=0`
`implies" "x^(2)-12x-2x+24=0impliesx(x-12)-2(x-12)=0`
`implies" "(x-12)(x-2)=0impliesx-12=0" or "x-2=0`
`implies" "x=12" or "x=2`
`implies" "x=12" "[because" "x=2implies(x-6)lt0]`
Hence, B alone can finish the work in 12 days.