Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the following problem : Find x if Paasche’s Price Index Number is 140 for the following data. - Mathematics and Statistics

Sum

Solve the following problem :

Find x if Paasche’s Price Index Number is 140 for the following data.

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 20 8 40 7
B 50 10 60 10
C 40 15 60 x
D 12 15 15 15
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Solution

Commodity Base Year Current Year p0q1 p1q1
  p0 q0 p1 q1    
A 20 8 40 7 140 280
B 50 10 60 10 500 600
C 40 15 60 x 40x 60x
D 12 15 15 15 180 225
Total 40x + 820 60x + 1105

From the table,
`sum"p"_0"q"_1 = 40x + 820, sum"p"_1"q"_1 = 60x + 1,105`

Paasche’s Price Index Number:

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

∴ 140 = `(60x + 1105)/(40x + 820) xx 100`  ...[P01(P) = 140]

∴ `(140)/(100) = (60x + 1,105)/(40x + 820)`

∴ `(7)/(5) = (60x + 1,105)/(40x + 820)`

∴ 280x + 5,740 = 300x + 5,525
∴ 300x – 280x = 5,740 – 5,525
∴ 20x = 215
∴ x = 10.75

  Is there an error in this question or solution?
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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 4.12 | Page 93
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