a and b can separately do a piece of work in 20..., Time & Work, General Mathematics

Question:A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be :

A `60` 
B `40` 
C `35` 
D `30`

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+ AnswerB

+ Explanationsolution:
`(A + B)'s 6` day's work `= 6(1/20 + 1/15)`
                                 `= 7/10`.
`(A + C)'s 4` day's work `= 3/10`.
`(A + C)'s 1` day's work `= 3/40`
`A's 1` day's work `= 1/20`
`:. C's 1` day's work `=(3/40 - 1/20)`
                             `=1/40`.
Hence, C alone can finish the work in `40` days.

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