# Solve the following problem : Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data - Mathematics and Statistics

Sum

Solve the following problem :

Find x if Laspeyre’s Price Index Number is same as Paasche’s Price Index Number for the following data

 Commodity Base Year Current Year Price p0 Quantity q0 Price p1 Quantity q1 A 3 x 2 5 B 4 6 3 5

#### Solution

 Commodity Base Year Current Year p0q0 p0q1 p1q0 p1q1 p0 q0 p1 q1 A 3 x 2 5 3x 15 2x 10 B 4 6 3 5 24 20 18 15 Total – – – – 3x + 24 35 2x + 18 25

From the table,
sum"p"_0"q"_0 = 3x + 24, sum"p"_0"q"_1 = 35,

sum"p"_1"q"_0 = 2x + 18, sum"p"_1"q"_1 = 25
Laspeyre’s Price Index Number:

P01(L) = (sum"p"_1"q"_0)/(sum"p"_1"q"_0) xx 100 = (2x + 18)/(3x + 24) xx 100          ...(i)

Paasche’s Price Index Number:

P01(P) = (sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100 =  (25)/(35) xx 100 = (5)/(7) xx 100                ...(ii)

Since P01(L) = P01(P),

(2x + 18)/(3x + 24) xx 100 = (5)/(7) xx 100    ...[From (i) and (ii)]

∴ (2x + 18)/(3x + 24) = (5)/(7)

∴ 14x + 126 = 15x + 120
∴ 126 – 120 = 15x – ·14x
∴ x = 6.

Concept: Construction of Index Numbers - Weighted Aggregate Method
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.1 | Page 93