# 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

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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 Quantityq0 Pricep1 Quantityq1 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,

sump_0q_0 = 3x + 24,

sump_0q_1 = 35

sump_1q_0 = 2x + 18,

sump_1q_1 = 25

Laspeyre’s Price Index Number:

P01(L) = (sump_1q_0)/(sump_0q_0) xx 100

= (2x + 18)/(3x + 24) xx 100      ...(i)

Paasche’s Price Index Number:

P01(P) = (sump_1q_1)/(sump_0q_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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Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]

#### 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
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