# The index numbers of food and clothing among the different groups of cost of living are 150 and 224.7

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The index numbers of food and clothing among the different groups of cost of living are 150 and 224.7 respectively for the year 2015. The price of fuel has increased by 220%. The expense on rent has increased from ₹ 4000 to ₹ 6000 and miscellaneous expenses increased by 1.75 times. If the expenditure for the first four groups are 40%, 18%, 12 % and 20 % respectively, find the cost of living index number for the year 2015 and interpret it.

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Index number of fuel = 100 + increase of 220% for the year 2015 = 320

Index number of rent for the year 2015 = $\cfrac{6000}{4000} × 100$ = 150

Index number of miscellaneous expenses for the year

= 100 + (100 × 1.75) = 100 + 175 = 275

Percentage expenditure on miscellaneous expenses = 100-(40 + 18 + 12 + 20) = 100 – 90 = 10 Cost of living index number for the year 2015

$I = \frac{ΣIW}{ΣW}$

$= \cfrac{19634.6}{100}$

= 196.35

Interpretation: There is (196.35 – 100=) 96.35% increase in the cost of living expenditure of the year 2015 as compared to the base year.