the consumer price index for June 2005 was 125.the food index was 120 and that of other items 135.what is the total weight given to food?
|
Items |
Index |
Weights |
WI |
|
Food |
120 |
W1 |
120 W1 |
|
Other Items |
135 |
W2 |
135 W2 |
|
|
|
|
|
Let the total weight = 100
W1 denotes weight of food
W2 denotes weight of food other items
So, W1 + W2 = 100 (i)
CPI = 125
12500 = 120 W1 + 135 W2 (ii)
Subtracting equations (ii) from (i)
|
13500 |
= |
135 W1 |
+ |
135 W2 |
|
12500 |
= |
120 W1 |
+ |
135 W2 |
|
– |
|
– |
|
– |
|
1000 |
= |
15 W1 |
|
|
Substituting the value of W1 in the equation (i)
W1 + W2 = 100
Or, 66.67 + W2 = 100
W2 = 33.33
Percentage of total weights given to food is 66.67% and other items is 33.33%