# Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data. Commodity Base Year Current Year Price Quantity Price Quantity A 1 10 2 5 B 1 5 – 12 - Mathematics and Statistics

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Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.

 Commodity Base Year Current Year Price Quantity Price Quantity A 1 10 2 5 B 1 5 – 12

#### Solution

Let us denote the missing value by x and reconstruct the table as follows.

 Commodity Base Year Current Year p0q0 p1q0 p1q1 p0q1 p0 q0 p1 q1 A 1 10 2 5 10 20 10 5 B 1 5 x 12 5 5x 1 12 Total 15 20 + 5x 10 + 12x 17

The above table gives

sum"p"0"q"_0 = 15, sum"p"_1"q"_0 = 20  5x, sum"p"_1"q"_1 = 10 + 12x, sum"p"_0"q"_1 = 17

It is given that

P01(L) = P01(P)

(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100

(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100

∴ (5x + 20)/15 = (12x + 10)/17

∴ (5(x + 4))/15 = (12x + 10)/17

∴ 17(x + 4) = 3(12x + 10)

∴ 17x + 68 = 36x + 30

∴ x = 2

Concept: Construction of Index Numbers - Weighted Aggregate Method
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Chapter 2.5: Index Numbers - Q.4
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