B can do a job twice as fast as A and half as fast as C.A.B. and C together take 16 days to complete it. In many days can C alone complete it ?

Options

A. 25
B. 42
C. 35
D. 28

Answer

D

Explanation

Let A can complete the job in x days. Then B can complete it in x/2 days and C can
complete it in x/4 days. Work done by A,B and C together in one day
`=(1)/(x)+(2)/(x)+(4)/(x)=(1)/(16)`
`implies (7)/(x)=(1)/(16)`
implies x=112`
`:.` C alone can complete it in `(112)/(4)`, i.e. 28 days.