a can do a piece of work in 14 days which b..., Time & Work, General Mathematics

Question:A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves  off. The total number of days to complete the work is :

A `6 3/5` 
B `8 1/2` 
C `10 1/5` 
D `13 1/2`

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+ AnswerC

+ Explanationsolution:
B's 3 day's  work =`(1/21 xx 3)`
                            = `1/7`.
Remaining work =`(1 - 1/7)`
                          = `6/7`
`(A + B)`'s 1 day's work = `(1/14 + 1/21)`
                                       =`5/42`.
Now, `5/42` work is done by A & B in 1 day.
`:. 6/7` work in done by A &  B in `(42/5 xx 6/7)`
                                                      =`36/5` days.
`:.` Total time taken = `(3 + 36/5)` days 
                                 = `10 1/5` days.

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