Y can complete a job half as fast as X and twice as fast as Z,X,Y and Z takes 8 days to complete it. In how many days can Y alone complete it?

Options

A. 21
B. 28
C. 35
D. 42

Answer

B

Explanation

Let the time taken by Y to complete the work be y days. Let the times taken by X and Z to complete it be x days and z days respectively.
`(1)/(y)=(1)/(2)((1)/(x))=2((1)/(z))`
`(1)/(y)=(1)/(2x) implies(1)/(x)=(2)/(y)`
`(1)/(y)=2(1)/(z)implies(1)/(z)=(1)/(2y)`
`(1)/(x)+(1)/(y)+(1)/(z)=(1)/(8)`
`(2)/(y)+(1)/(y)+(1)/(2y)=(1)/(8)`
`(7)/(2y)=(1)/(8)`
y=28