a and b can do a piece of work in 5 days..., Time & Work, General Mathematics

Question:A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. Who among these will take the least time if put to do it alone ?

A A 
B B 
C C 
D Data inadequate

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+ AnswerA

+ Explanationsolution:
`(A + B)`'s 1 day's work = `1/5`;
`(B + C)`'s 1 day's work = `1/7` and
`(A + C)`'s 1 day's work = `1/4`.
`2(A + B + C)`'s 1 day's work =`(1/5 + 1/7 + 1/4)`
                                                =`83/140`.
`(A + B + C)`'s 1 day's work = `83/280`.
 C's 1 day's work =`(83/280 - 1/5)`
                            = `27/280`.
 A's 1 day's work =`(83/280 - 1/7)`
                           =`43/280`.
 B's 1 day's work =`(83/280 - 1/4)`
                           =`13/280.`
Thus time taken by A, B, C is `280/43` days, `280/13` days, `280/27` days respectively.
Clearly, the time taken by A is least.

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