Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
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 
p0
Quantity
q0
Price
p1
Quantity
q1
A 3 x 2 5
B 4 6 3 5
Advertisement Remove all ads

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,
`sum"p"_0"q"_0 = 3x + 24, sum"p"_0"q"_1 = 35`,

`sum"p"_1"q"_0 = 2x + 18, sum"p"_1"q"_1 = 25`
Laspeyre’s Price Index Number:

P01(L) = `(sum"p"_1"q"_0)/(sum"p"_1"q"_0) xx 100 = (2x + 18)/(3x + 24) xx 100`          ...(i)

Paasche’s Price Index Number:

P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_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?
Advertisement Remove all ads

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
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×