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

Question:A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed ?

A `10 1/2` 
B `10 1/3` 
C `10 1/4` 
D `10 2/3`

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+ AnswerC

+ Explanationsolution:
`(A + B)'s 2` day's work `= (1/9 + 1/12)`
                                  `= 7/36`.
Work done in 5 pairs of days `= (5 xx 7/36)`
                                        `= 35/36`.
Remaining work `= (1 - 35/36)`
                     `= 1/36`.
On 11th day, it is A's turn.
`1/9` work is done by him in 1 day.
`1/36` work id done by him in `(9 xx 1/36)`
                                         `= 1/4`day.
`:.`Total time taken `= 10 1/4` days.

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