Question

An enquiry into the budgets of the middle class families in a certain city gave the following information

$\begin{array}{cccccc}\text{Expenses on items}& \text{Food}& \text{Fuel}& \text{Clothing}& \text{Rent}& \text{Miscellaneous}\\ & 35\%& 10\%& 20\%& 15\%& 20\%\\ \text{Price (in Rs ). in 2004}& 1500& 250& 750& 300& 400\\ \text{Price (in Rs ). in 1995}& 1400& 200& 500& 200& 250\end{array}$

What is the cost of living index of 2004 as compared with 1995?

Answer 1

$\begin{array}{cccccc}\text{Items}& \text{Weight (W)}& \text{Price in 1995}\left(P_0\right)& R=\frac{P_1}{P_0}\times 10& \text{WR}& \\ \text{Food}& 35& 1400& 1500& \frac{1500}{1400}\times 100=107.14& 3749.90\\ \text{Fuel}& 10& 200& 250& \frac{250}{250}\times 100=125& 1250\\ \text{Clothing}& 20& 500& 750& \frac{750}{500}\times 100=150& 3000\\ \text{Rent}& 15& 200& 300& \frac{300}{200}\times 100=150& 2250\\ \text{Miscellaneous}& 20& 250& 400& \frac{400}{250}\times 100=160& 3200\\ & \sum =100& & & \sum WR=13449.9& \end{array}$

CPI = $\frac{\sum WR}{\sum W}$

= $\frac{13449.9}{100}$

= 134.49

Cost of living index = 134.50

Thus the price rose by 34.50 during 1995 and 2004.