A and B can do a piece of work in 30 days, while B and C can do the same work in

CuriousTab

Question
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Options
A. 18 days
B. 24 days
C. 30 days
D. 36 days

Correct Answer

18 days

Explanation

2(A + B + C)'s 1 day's work =	❨	1	+	1	+	1	❩	=	15	=	1	.
		30		24		20			120		8

Therefore, (A + B + C)'s 1 day's work =	1	=	1	.
	2 x 8		16

Work done by A, B, C in 10 days =	10	=	5	.
	16		8

Remaining work =	❨	1 -	5	❩	=	3	.
			8			8

A's 1 day's work =	❨	1	-	1	❩	=	1	.
		16		24			48

Now,	1	work is done by A in 1 day.
	48

So,	3	work will be done by A in	❨	48 x	3	❩	= 18 days.
	8				8