a and b can do a piece of work in 72 days..., Time & Work, General Mathematics

Question:A and B can do a piece of work in 72 days; B and C do it in 120 days; A and C can do it in 90 days. In what time can A alone do it ?

A 150 days 
B 120 days 
C 100 days 
D 80 days

/47

+ AnswerB

+ Explanationsolution:
`(A + B )`'s 1 day's work =`1/721`,
`(B + C)`'s  1day's work =` 1/120`,
`(A + C)`'s  1day's work =`1/90`.
Adding `2(A + B + C)`'s 1 day's work = `(1/72 + 1/120 + 1/90)`
                                                            =`12/360`
                                                            =`1/30`.
`:. (A + B + C)`'s 1 day's work =`1/60`.
     A's 1 day's work =`(1/60 - 1/120)`
                               =`1/120`.
`:.` A alone can finish the work in 120 days.

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