Question

Alekh and alia can together do a piece of work in 5 days which alia and aman together can do in 15 days. After alekh has been working at it for 4 days and alia for 5 days, aman then takes up and completes the work alone in 4 days. In how many days can alia do the work alone?

Answer 1

Answer:

Alia alone do the work in 45 Days

Step-by-step explanation:

Let say Alekh  Can complete work in X days

=> Alekh 1 day work = 1/X

Let say Alia  Can complete work in Y days

=> Alia 1 day work = 1/Y

Let say Aman  Can complete work in Z days

=> Aman 1 day work = 1/Z

Alekh and alia can together do a piece of work in 5 days

=> 5/X  + 5/Y  = 1

=> 5/X = 1 - 5/Y

alia and aman together can do in 15 days

15/Y + 15/Z = 1

Alekh 4 days work = 4/X

Alia 5 Days Work = 5/Y

Aman 4 Days Work = 4/Z

4/X  + 5/Y  + 4/Z  = 1

4/X + 4/Z = 1 - 5/Y

=> 4/X  + 4/Z = 5/X

=> 4/Z = 1/X

=> Z = 4X

15/Y  + 15/4X = 1

5/X  + 5/Y  = 1

15/Y + 15/4X  = 5/X  + 5/Y

=> 10/Y = 5/4X

=> Y = 8X

5/X  + 5/Y  = 1

=>5/X  + 5/8X = 1

=> 45 = 8X

=> X = 45/8

=> Y = 45

=> Z = 45/2

Alia alone do the work in 45 Days