Question

The price of wheat increased by 70 % and price of rice increased by 40 % in the year 2015 with respect to the year 2010. The price of bajri decreased by 25 %. The price of oil increased by 40 % and the price of ghee decreased by 5 %. If the importance of oil is three times and of rice is double that of ghee and the importance of each of wheat and bajri is double that of rice, find price index number of the group of these five items and interpret it.

Answer 1

Here, percentage increase or decrease in the prices of food items are given.

∴ Index number of the item

= 100 + % increase OR

= 100 – % decrease

∴ Suppose, importance of ghee is 1.

∴ the importance of oil is 3 × 1 = 3

and that of rice is 2 × 1 = 2

The importance of wheat and bajri each is double the importance of rice,

∴ the importance of wheat is 2 × 2 = 4

and that of bajri is 2 × 2 = 4

General index number of price

\(I=\frac{\sum IW}{\sum W}\)

\(=\frac{1775}{14}=126.79\)

Hence, price index of a group of five items is obtained 126.79.

Interpretation: There is 26.79 % in the prices of five items of the group.