Maharashtra State BoardHSC Commerce 12th Board Exam
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Calculate the cost of living index in problem - Mathematics and Statistics

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Sum

Calculate the cost of living index in problem 

Group Base Year Current Year
  Price Quantity Price
Food 120 15 170
Clothing 150 20 190
Fuel & Lighting 130 30 220
House Rent 160 10 180
Miscellaneous 200 12 200
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Solution

Group Base Year Current Year p1q0 p0q0
  p0 q0 P1    
Food 120 15 170 2550 1800
Clothing 150 20 190 3800 3000
Fuel & Lighting 130 30 220 6600 3900
House Rent 160 10 180 1800 1600
Miscellaneous 200 12 200 2400 2400
Total 17150 12700

From the table,
`sum"p"_1"q"_0 = 17,150, sum"p"_0"q"_0 = 12,700`
Now, by Aggregate Expenditure Method,

CLI = `(sum"P"_1"q"_0)/(sum"p"_0"q"_0) xx 100`

= `(17150)/(12700) xx 100`
= 135.04

Concept: Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
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