Q.4. Due to change in prices, the cost of living index for the working class in a city rose to 225 in April from 180 in March, 2003. The index of food became 252 from 198, that of clothing from 185 to 205, that of fuel and lighting from 175 to 195 and that of miscellaneous from 138 to 212. The index of rent, however remained unchanged at 150. Find the weights of all the groups if the weights of clothing, fuel and lighting, and rent were the same.
Hint. Construct the following table :

Dear studentWeighted mean is given by i=1n Xi wii=1n wi, where wi is the wieghtIn march, it is giveni=1n Xi wii=1n wi=180198×x+185×1+175×1+150×1+138×yx+1+1+1+y=198x+185+175+150+138yx+3+y=180198x+510+138y=180x+540+180y18x-42y=303x-7y=5 _______________1In April, it is giveni=1n Xi wii=1n wi=225252×x+205×1+195×1+150×1+212×yx+1+1+1+y=252x+205+195+150+212yx+3+y=225252x+550+212y=225x+675+225y27x-13y=125 __________2From equation 1x=5+7y3Put in equation 227×5+7y3-13y=12545+63y-13y=12550y=80y=8050=85x=5+7×853=5+5653=8115=275

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