Question
A and B together can do a work in 10 days, B and C can
do together in 5 days while C and A together can do in 12 days. In how many days C alone will complete the work?Solution
(A + B)’s 1 day’s work = 1/10 (B + C)’s 1 day’s work = 1/5 (C + A)’s 1 day’s work = 1/12 2 (A +B + C)’s 1 day’s work = 1/10 + 1/5 + 1/12 = (6+12+5)/60 = 23/60 ∴ (A + B + C)’s 1 day’s work = 23/120 Now, C’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + B)’s 1 day’s work, => 23/120 – 1/10 = 11/120 Therefore C will finish the work in = 120/11 = 
days.
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