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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

#### 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 |

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 = p_{0}q_{0}

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 |