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
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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

RELATED QUESTIONS

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

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 70 90 100 60 80
W 5 3 2 4 6

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

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I 400 300 150 120 100
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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:

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 200 150 120 180 160
W 30 20 10 40 50

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

Find x if the cost of living index is 150.

Group Food Clothing Fuel & Lighting House Rent  Miscellaneous
I 180 120 300 100 160
W 4 5 6 x 3

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

Solve the following problem :

Find the cost living index number by the Weighted Aggregate Method.

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 78 80 110 60 90
W 5 3 4 2 6

Solve the following problem :

Find the cost of living index number by Family Budget Method for the following data. Also, find the expenditure of a person in the year 2008 if his expenditure in the year 2005 was ₹ 10,000.

Group Base Year
(2005) Price
Current Year
(2008) Price
Weight
Food 12 60 25
Clothing 10 45 20
Fuel and Lighting 20 35 15
House Rent 25 20 30
Miscellaneous 16 48 10

Solve the following problem :

Find x if the cost of living index number is 193 for the following data.

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 221 198 171 183 161
W 35 14 x 8 20

Choose the correct alternative:

The Cost of Living Index Number using Weighted Relative Method is given by


State whether the following statement is True or False:

For Cost of Living Index Number CLI =`(sum"IW")/(sum"W")`, where I = `("P"_0)/("P"_1) xx 100` and w = p0q0


Calculate the Cost of Living Index by Family Budget method in following example where W are wages of base year and I are current year price relatives.

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

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