A and B together can do a piece of work in 30 days, B and

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A and B together can do a piece of work in 30 days, B and C together can do it in 20 days. A starts the work and works on it for 5 days, then B takes it up and works for 15 days. Finally C finishes the work in 18 days. In how many days can C do the work when doing it separately?

Let us denote A’s 1 day’s work by A, B’s 1 day’s work by B and C’s work by C.

So, A + B =	1
	30

and B + C =	1
	20

Also, 5A + 15B + 18C = 1 work.
This can be written as,
5 (A + B) + 10 (B + C) + 8C= 1
Substituting the values of (A + B) and (B + C) we get,

=		5 ×	1		+		10 ×	1		+ 8C = 1
			30					20

or	1	+	1	+ 8C = 1
	6		2

or 8C = 1 -	1	-	1
	6		2

or 8C =	6 - 1 - 3
	6

or 8C =	2
	6

or C =	2	=	1
	6 × 8		24

Hence, C will complete the work in 24 days.