The following data relates to a household's spending on four items. Compute the Cost of Living Index for the current year. | Item | $p_0$ (Rs.) | $p_1$ (Rs.) | Weight $W$ (%) | |---|---|---|---| | Food | 60 | 78 | 45 | | Rent | 100 | 115 | 30 | | Clothing | 30 | 36 | 15 | | Miscellaneous | 20 | 25 | 10 |

The following data relates to a household's spending on four items. Compute the Cost of Living Index for the c

Practice Questions · Q7

The following data relates to a household's spending on four items. Compute the Cost of Living Index for the current year.

Item	$p_0$ (Rs.)	$p_1$ (Rs.)	Weight $W$ (%)
Food	60	78	45
Rent	100	115	30
Clothing	30	36	15
Miscellaneous	20	25	10

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First compute each item's price relative:

I_{\text{Food}}=\dfrac{78}{60}\times100=130,\quad I_{\text{Rent}}=\dfrac{115}{100}\times100=115

I_{\text{Clothing}}=\dfrac{36}{30}\times100=120,\quad I_{\text{Misc}}=\dfrac{25}{20}\times100=125

Multiply each by its own weight $W$ :

$130(45)=5850,\quad 115(30)=3450,\quad 120(15)=1800,\quad 125(10)=1250$ …