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
Quantity
q0
Price
p1
Quantity
q1
A 3 x 2 5
B 4 6 3 5
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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
  Is there an error in this question or solution?
Chapter 5: Index Numbers - Miscellaneous Exercise 5 [Page 93]
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