A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?	Choose the most appropriate option.
A) 24	B) 6	C) 5	D) 4	E) 3
As A and B can finish the work in 12 days time, hence   (A + B)’s one day’s work = 1/12;   similarly   (B + C)’s one day’s work = 1/16   Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1   A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1   Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1   i.e. 5/12 + 2/16 + C’s 11 days’ work = 1   or C’s 11 days’ work = 1 - (5/12 + 2/16)   or C’s 11 days’ work = 1 - 13/24   or C’s 11 days’ work = 11/24   or C’s 1 day’s work = 11/24 x 1/11 = 1/24   Therefore, C alone can finish the complete work in 24 days.   24NSWER:24
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A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?