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Question
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
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:
| Group | Food | Clothing | Fuel & Lighting | House Rent | Miscellaneous |
| I | 400 | 300 | 150 | 120 | 100 |
| W | 3 | 3 | 4 | 5 | 2 |
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 |
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 |
