The consumer price index for June, 2005 was 125

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#1

The consumer price index for June, 2005 was 125. The food index was 120 and that of others
items 135. What is the percentage of the total weight given to food?


#2

Let X denote the percentage of total weight given to food and 100 - X denote the percentage of total weight given to other items.
CPI = 120x135(100-X) / 100

12500 = 120X +13500 - 135X
=> 1000 = 152X ====>X= 1000/15 = 66.67% .

Thus, the percentage of the total weight given food = 66.67%