Question

Varun takes 6 days less than the time taken by sachin to finish a piece of work. if both varun and sachin together can finish it in 4 days, find the time taken by sachin to finish the work.

Answer 1

Let the time taken by Sachin is x days
So time taken by Varun will be x-6 days
One day work of Sachin = 1/x
One day work of Varun = 1/x-6
ATQ :

1/x-6+1/x = 4
=> (x+x-6)/x²-6x = 4
=> 2x-6 = 4x²-24x }dividing by 2

=> x-6=2x²-12x
=> 2x²-13x+6 =0
=> 2x²-12x-x+6 = 0
=> 2x(x-6)-1(x-6) = 0
=> (2x-1)(x-6) =0

2x-1 =0 => x=1/2

x-6=0 => x=6

I case [x=1/2]:

Varun's work = x-6=1/2-6 = -5.5

2 case [x= 6]:

Varun's work = x-6 = 6-6 =0

Work can't be -ve so x= 6days

Answer 2

Let Varun complete the work in 'X' days
Sachin takes 'X+6' days to complete the work.

In 1 day,
Varun does: 1/X work
Sachin does: 1/X+6 work
Both do: 1/4 work
1/X + 1/X+6 = 1/4
(X+6+X)/X*(X+6) = 1/4
4*(2X+6) = X*(X+6)
8X + 24 = X^2 + 6X
X^2 - 2X - 24 = 0
X^2 - 6X + 4X - 24 = 0
X(X-6) + 4(X-6) = 0
(X+4)*(X-6) = 0
Hence, X = 6
Sachin's time = X+6 = 12 days.
Hence, Sachin takes 12 days to complete the work 
Hope it helps.