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The cost of living index of the year 200...

The cost of living index of the year 2006, taking the year 2005 as the base year, is 225. The total expenditure in 2005 and 2006 are Rs. (2x+7y) and Rs. (7x+y) respectively, where x and y are positive integers. Which of the following can be the total expenditure in 2005 ? (in Rs.)

A

37600

B

47600

C

28400

D

27200

Text Solution

Verified by Experts

The correct Answer is:
A
`225=(7x+y)/(2x+7y)(100)`
450x+1575y=700x+100y
1475y=250x
5.9y=x
Total expenditure in 2006 (in Rs.) =2x+7y=2(5.9y)+7y=18.8 y
`=(188y)/(10)=(94y)/(5)`
y is a positive interger.
Only option (a) satisfies this condition.
`(therefore (94y)/(5) =37600 therefore y=2000`. In other options, y is not a positive integer).
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