Question

For doing some work Ganesh takes 10days more than Gajanan. If both work together,they complete the work in 12days. Find the number of days taken by Ganesh to complete the work,if he works alone.

Answer 1

Step-by-step explanation:

Let the no. of days taken by ganesh be x.

therefore, no. of days take by gajajan is x-10

Work done by ganesh in one day is

1 / x and work done by gajanan is 1 / x - 10

Time taken to do the work together is 12 days Work done together in one day - 1 / 12

ATQ,

1 / x-10 + 1 / x = 1 / 12

Take LCM

12 ( 2x - 10) = x ( x - 10)

24x - 120 = x ^2 - 10x

x ^2 - 34x + 120 = 0

x ^ 2 - 30 x - 4x + 120 = 0

x ( x - 30) + 4 ( x - 30) = 0

( x +4 ) ( x - 30) = 0

x = 30, - 4

The answer is 30 because days cannot be negative.

Therefore days taken to do the work by ganesh is 30 days.

Hence Proved.