Quadratic Equations

let A takes x days to complete the work.

so one day's work by A is 1/x

B takes 16 days less , i.e. he takes x-16 days.

so B's one day's work is 1/(x-16)

together they finish the work in 15 days, so their one day's work together is 1/15

so ATQ,

1/x+1(x-16)=1/15

solving we get

(x-40)(x-6)=0

so x=40 as x =6 can't be taken becouase then x-16 becomes a negative number.

so A takes 40 days to complete the work

so,

B takes 40-16=24 days to complete the work