A can do a piece of work in 16 days and B in 24 days. They

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A can do a piece of work in 16 days and B in 24 days. They take the help of C and three together finish the work in 6 days. If the total remuneration for the work is ₹ 400. The amount (in rupees)each will receive, in proportion, to do the work is

1. A : 150, B : 100, C : 150
2. A : 100, B : 150, C : 150
3. A : 150, B : 150, C : 100
4. A : 100, B : 150, C : 100

Rule 3 and Rule 25,
If C alone completes the work in x days, then

=	1	+	1	+	1	=	1
	16		24		x		6

⇒	1	=	1	-	1	-	1
	x		6		16		24

=	8 - 3 - 2	=	1
	48		16

⇒ x = 16 days
∴ Ratio of their remuneration

=	1	:	1	:	1	= 3 : 2 : 3
	16		24		16

∴ A’s remuneration

=	3	× 400 = ₹ 150
	8

B’s remuneration

=	2	× 400 = ₹ 100
	8

C’s remuneration

=	3	× 400 = ₹ 150
	8

⇒ A : 150, B : 100, C : 150