Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

5 : 7 : 8
20 : 49 : 64
38 : 28 : 21
None of these

Correct Answer: 20 : 49 : 64

Explanation:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now,	14x	=	5	⟺ 98x = 40y ⟺ y =	49	x
	8y		7		20

And,	14x	=	5	⟺ 112x = 35z ⟺ z =	112	x =	16	x.
	7z		8		35		5

∴ x : y : z = x :	49	x	:	16	x	= 20 : 49 : 64.
	20			5

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