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Solve the following problem : Given that ∑p1q1=300,∑p0q1=320,∑p0q0 = 120, and Marshall- Edgeworth’s Price Index Number is 120, find ∑p1q0 and Paasche’s Price Index Number. - Mathematics and Statistics

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Question

Solve the following problem :

Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.

Sum
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Solution

Given, P01(M-E) = `120, sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0 = 120`

P01(M–E) = `(sum"p"_1"q"_0 + sum"p"_1"q"_1)/(sum"p"_0"q"_0 + sum"p"_0"q"_1) xx 100`

∴ 120 = `(sum"p"_1"q"_0 + 300)/(120 + 320) xx 100`

∴ 120 = `(sum"p"_1"q"_0 + 300)/(440) xx 100`

∴ `sum"p"_1"q"_0 + 300 = (120 xx 440)/(100)`

∴ `sum"p"_1"q"_0 + 300` = 528
∴ `sum"p"_1"q"_0` = 528 – 300
∴ `sum"p"_1"q"_0` = 228

Paasche’s Price Index Number:

P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

= `(300)/(320) xx 100`
= 93.75

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Construction of Index Numbers - Weighted Aggregate Method
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Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]

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Balbharati Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.17 | Page 93

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