3 persons undertake to complete a piece of work for $1,200.

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3 persons undertake to complete a piece of work for $1,200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get?

Let the fourth person complete the entire work in D days.
Given :- Total amount = $1,200
Now, according to the question,

3	+	3	+	3	+	3	=	1
8		12		16		D

⇒	1	=	1	-	1	-	1	-	1	=	16 - 6 - 4 - 3	=	1
	D		3		8		12		16		48		16

∴ D = 16

Ratio of wages =	1	:	1	:	1	:	1	=	6 : 4 : 3 : 3
	8		12		16		16

Sum of ratios = 6 + 4 + 3 + 3 = 16

∴ Fourth person’s share =	Fourth person’s ratio	x Total amount
	Sum of all ratios

Fourth person’s share =	3	x 1200 = $ 225.
	16