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

Question:A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is :

A `4` 
B `8` 
C `12` 
D `24`

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+ AnswerD

+ Explanationsolution:
Suppose the work was finished in `x` days.
Then A's `(x - 8)` day's work `+ B's (x - 12)` day's work `+ C's x` day's work `= 1`
 `(x - 8)/36 + (x - 12)/54 + x/72 = 1 iff 6(x - 8) + 4(x - 12) + 3x = 216`
`:. 13x = 312 iff x = 24`.

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