Question

Takes 6 days less than q to finish the work individually. if p and q working together complete the work in 4 days, then how many days are required by q to complete the work alone ?

Answer 1

let p takes x days

so p's work in a day = 1/x

q requires x+6 days

so q's work in a day = 1/x+6

now

1/x + 1/x+6 = 1/4

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

x(x+6) = 8x + 24

x^2 +6x = 8x + 24

x^2 +6x - 8x - 24 = 0

x^2 - 2x - 24 = 0

x^2 - 6 x + 4x - 24 = 0


x ( x - 6 ) + 4 ( x -6 ) = 0

( x - 6 ) ( x + 4) = 0

( x - 6 ) = 0 or ( x + 4) = 0

x = 6 or x = -4

days never negative so x = -4 not possible


so , x = 6 days

p takes 6 days

and q takes 6+6 = 12 days