Pintu takes 6 days more than those of Nishu to complete certain work. If they work togeter they finish it in 4 days. How many days would it take to complete the work if they work alone.

Answer

Nishu takes 6 days and Pintu takes 12 days to complete the work individually.

Explanation

Let Nishu take x days to complete the work. Then Pintu takes (x+6) days to complete the same work.
In one day, Nishu does `(1)/(x)` part of the work and Pintu does `(1)/(x+6)` part of the work.
`:.` in 1 day they together do `((1)/(x)+(1)/(x+6))` part of the work
`(1)/(x)+(1)/(x+6)=(x+6+x)/(x(x+6))=(2x+6)/(x^(2)+6x)`
`:.` total number of days taken by them together to complete the work is `(x^(2)+6x)/(2x+6)`
From the given condition,
`(x^(2)+6x)/(2x+6)=4" ":.x^(2)+6x=4(2x+6)`
`:.x^(2)+6x=8x+24" ":.x^(2)+6x-8x-24=0`
`:.x^(2)-2x-24=0" ":.x^(2)-6x+4x-24=0`
`:.x(x-6)+4(x-6)=0" ":.(x-6)(x+4)=0`
`:.x-6=0orx+4=0" ":.x=6orx=-4`
But the number of days cannot be negative.
`:.x=-4` is unacceptable.
`:.x=6" "x+6=6+6=12`