Quantitative Aptitude :: Time and Work - Discussion

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Explanation:
(A and B) 1 day work = 1/12 -----(1)
(B and C) 1 day work = 1/16 -----(2)

Given A's 5 days' work + B's 7 days' work + C's 13 days' work = 1
simplify the above ..
=> (A + B)'s 5 days' work + (B + C)'s 2 days' work + C's 11 days' work = 1

Put the values from equation (1) & (2)
=> (5*1/12)+(2*1/16) + C's 11 days' work = 1

=> C's 11 days' work = (1-5/12+2/16)=11/24

=> C's 1 day's work = (11/24?1/11)=1/24

So C alone can finish the work = 24 days.