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Question
The consumer price index for June 2005 was 125. The food index was 120 and that of other items 135. What is the percentage of the total weight given to food?
Solution
|
Items |
Index |
Weights |
WI |
|
Food |
120 |
W1 |
120 W1 |
|
Other Items |
135 |
W2 |
135 W2 |
| ∑W = 100 | ∑WI = 120W1 + 135W2 |
Let the total weight = 100
W1 denotes the weight of food
W2 denotes the weight of food other items
So, W1 + W2 = 100 (i)
CPI = 125
CPI = `(sumWR)/(sumW)`
125 = `(120W_1 + 135W_2)/100`
12500 = 120 W1 + 135 W2 (ii)
Subtracting equations (ii) from (i)
|
13500 |
= | 135 | + | 135 |
| W1 | W2 | |||
| 12500 | = | 120 | + | 135 |
| W1 | W2 | |||
| - | - | - | ||
| 1000 | = | 15 | ||
| W1 |
So, `W_1 = 1000/15 = 66.67`
Substituting the value of W1 in the equation (i)
W1 + W2 = 100
Or, 66.67 + W2 = 100
W2 = 33.33
The percentage of total weights given to food is 66.67% and other items are 33.33%.
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