# Find the missing wage if the Cost of Living Index for the following data is 150. Group Food Clothing Fuel and Lighting House Rent Miscellaneous I 200 150 140 100 120 W 6 4 x 3 4 - Mathematics and Statistics

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Find the missing wage if the Cost of Living Index for the following data is 150.

 Group Food Clothing Fuel and Lighting House Rent Miscellaneous I 200 150 140 100 120 W 6 4 x 3 4

#### Solution

Construct the following table:

 Group I W IW Food 200 6 1200 Clothing 150 4 600 Fuel and Lighting 140 x 140x House Rent 100 3 300 Miscellaneous 120 4 480 Total 17 + x 2580 + 140x

From the table,

sum"W" = 17 + x sum"IW" = 2580 + 140x

Now, by family budget method,

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

∴ 150 = (2580 + 40x)/(17 + x)

∴ 150 × 17 + 150x = 2580 + 140x

∴ 2550 + 150x = 2580 + 140x

∴ 150x – 140x = 2580 – 2550

∴ 10x = 30

∴ x = 3

Concept: Method of Constructing Cost of Living Index Numbers - Family Budget Method
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Chapter 2.5: Index Numbers - Q.4
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