Let Anil takes x number of days to complete the work
⇒1 day =1x of the work.
Sunil takes 5 more days than Anil to complete the work.
⇒1 day =1(x+5) of the work
1 day =1x+1x+5
1 day =(x+5+x)x(x+5)
1 day =(2x+5)(x2+5x) of work done
To find 4 days of work done:
1 day =(2x+5)(x2+5x)
4 days =(8x+20)(x2+5x) of work done
To find the amount of work left to be done:
Work left =1−(8x+20)(x2+5x)
Work left =(x2+5x−8x−20)(x2+5x)
Work left =(x2−3x−20)(x2+5x)
Solving for x:
Give that Anil needs 5 days to complete the rest of the work
∴x=10 or x=−2 (Rejected, number of days cannot be negative)
To find the number of days each take to complete the work
Anil =x=10 days
Sunil =x+5=10+5=15 days
Thus, Anil takes 10 days and Sunil takes 15 days to complete the work.