# Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in: Find y if the cost of living index is 200. - Mathematics and Statistics

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Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Find y if the cost of living index is 200.

 Group Food Clothing Fuel & Lighting House Rent Miscellaneous I 180 120 160 300 200 W 4 5 3 y 2

#### Solution

 Group I W IW Food 180 4 720 Clothing 120 5 600 Fuel & Lighting 160 33 480 House Rent 300 y 300y Miscellaneous 200 2 400 Total – y + 14 300y + 2200

From the table,
sum"W" = y + 14, sum"IW" = 300y + 2200
Now, by Family Budget Method,

CLI = (sum"IW")/(sum"W")

∴ 200 = (300y + 2200)/(y + 14)      ...[∵ CLI = 150]

∴ 200y + 2800 = 300 +2200
∴ 300y – 200y = 2800  – 2200
∴ 100y = 600
∴ y = (600)/(100)
∴ y = 6.

Concept: Method of Constructing Cost of Living Index Numbers - Family Budget Method
Is there an error in this question or solution?
Chapter 5: Index Numbers - Exercise 5.3 [Page 87]

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