a and b can do a piece of work in 45 days..., Time & Work, General Mathematics

Question:A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but a leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was :

A 6 
B 8 
C 9 
D 12

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+ AnswerC

+ Explanationsolution:
`(A + B)`'s 1 day's work = `(1/45 + 1/40)`
                                   =`17/360`.
Work done by B in 23 days = `(1/40 xx 23)`
                                       =`23/40`.
Remaining work = `(1 - 23/40)`
                       =`17/40`.
Now, `17/360` work was done by `(A + B)` in `(1 xx 360/17 xx 17/40)`
                                                                  = 9 days.
`:.`A left after 9 days.

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