To do a certain work, B would take time thrice as long as

Home » Aptitude » Time and Work » Question

To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is

1. 22 days
2. 24 days
3. 30 days
4. 20 days

Correct Option: B

Using Rule 2 and 3,
If B does the work in 3x days, (A + C) will do the same work in xdays.
If C does that work in 2y days.(A + B) will do it in y days.

	1	+	1	=	1
	x		3x		10

∴	4	=	1
	3x		10

⇒ 3x = 40

⇒ x =	40
	3

Again,	1	+	1	=	1
	y		2y		10

⇒	3	=	1
	2y		10

⇒ y =15
∴ (A + B + C)’s 1 day’s work

=	1
	10

⇒	1	+	1	+	1	=	1
	A		40		30		10

⇒	1	=	1	-	1	-	1
	A		10		40		30

=	12 - 3 - 4	=	5	=	1
	120		120		24

∴ A alone will complete the work in 24 days.