Question

Calculate the cost of living index number for the year 1995 on the basis of 1990 from the following data:

Item	Quantity (In Kg)	Cost (In Rs. per Kg) (Year 1990)	Cost (In Rs. per Kg) (Year 1995)
A	8	$30.00$	$45.00$
B	5	$28.00$	$36.00$
C	12	$6.00$	$11.00$
D	40	$9.00$	$15.00$
E	18	$10.00$	$12.00$

Answer 1

Here we will first write the basic equation of the cost of living index. Then we will find the value of total expense in the year 1995 and then we will find the value of total expense in the year 1990. We will then put these values in the formula of the cost of living index to find the required value.

Complete Step by Step Solution:
The data is given for the year 1990 and for the year 1995.
First we will find the value of total expense in the year 1995. Therefore, we get
Total expense in 1995 $= \left( {8 \times 45} \right) + \left( {5 \times 36} \right) + \left( {12 \times 11} \right) + \left( {40 \times 15} \right) + \left( {18 \times 12} \right)$
Multiplying the terms, we get
$\Rightarrow$ Total expense in 1995 $= 360 + 180 + 132 + 600 + 216 = 1488$
Now we will find the value of the total expense in the year 1990. Therefore, we get
Total expense in 1990 $= \left( {8 \times 30} \right) + \left( {5 \times 28} \right) + \left( {12 \times 6} \right) + \left( {40 \times 9} \right) + \left( {18 \times 10} \right)$
Multiplying the terms, we get
$\Rightarrow$ Total expense in 1990 $= 240 + 140 + 72 + 360 + 180 = 992$
We know that the cost of living index is equal to the ratio of the total expense in that year to the total expense in the reference year. So by solving that we will get the value of the cost of living index. Therefore, we get
Cost of living index $=$ (Total expense in1995 $\div$ Total expense in1995) $\times 100$……………………… $\left( 1 \right)$
Now we will put the value of total expense in 1995 and 1990 in the equation $\left( 1 \right)$ to get the value of the cost of living index. Therefore, we get
$\Rightarrow$ Cost of living index $= \dfrac{{1488}}{{992}} \times 100$
Multiplying the terms, we get
$\Rightarrow$ Cost of living index $= 150$

Hence the cost of living index number for the year 1995 on the basis of 1990 is equal to 150.

Note:
Cost of living index is that index which helps us measure the relative change in the prices of the goods on the basis of some previous year i.e. reference year. It is a theoretical price index and helps in understanding the inflation rate in the country. While calculating the cost of living index we should keep in mind that in the ratio, expense of that particular year is taken in the numerator of the ratio and reference year total expense in the denominator.