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Chart
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 p_{0} 
Quantity q_{0} 
Price p_{1} 
Quantity q_{1} 

A  3  x  2  5 
B  4  6  3  5 
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Solution
Commodity  Base Year  Current Year  p_{0}q_{0}  p_{0}q_{1}  p_{1}q_{0}  p_{1}q_{1}  
p_{0}  q_{0}  p_{1}  q_{1}  
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:
P_{01}(L) = `(sump_1q_0)/(sump_0q_0) xx 100`
= `(2x + 18)/(3x + 24) xx 100` ...(i)
Paasche’s Price Index Number:
P_{01}(P) = `(sump_1q_1)/(sump_0q_1) xx 100`
= `(25)/(35) xx 100`
= `(5)/(7) xx 100` ...(ii)
Since P_{01}(L) = P_{01}(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?