Question

Suresh and Nilesh started working together for a particular work. After working for 4 days Nilesh left the work Suresh continued further for 5 days but only half of the work is completed. If Nilesh alone takes 10 days less to finish work than Suresh. Find the number of days each can finish work alone.

Answer 1

Let Niresh take x days to complete the work
Suresh takes = (x+10) days. Niresh takes 10 days less

Fraction completed in a day:

Nilesh = 1/x
Suresh = 1/(x+10)

Total work completed in a day = 1/x + 1/(x+10) = (2x+10)/x(x+10)
Total work completed in 4 days = 4(2x+10)/x(x+10)

Suresh works alone for 5 days
Amount of work completed during this time = 5x 1/(x+10) = 5/(x+10)

Total work completed so far = 4(2x+10)/x(x+10) + 5/(x+10)
                                             = {4(2x+10) + 5x}/x(x+10)

But only half of the work is completed, so;

{4(2x+10) + 5x}/x(x+10) = 1/2

This simplifies to:

x^2 - 6x - 90 = 0 (a quadratic equation)

We use the quadratic formula

a=1
b = -6
c = -90

(Using ⊥ to stand for plus or minus)

x = {-(-6)⊥√(-6)² -4x1x(-90)} / 2x1
x = (6⊥20)/2

x = 13 or x = - 7
Take x = 13

∴ Nilesh takes 13 days
Suresh takes (13+10) = 23 days