# 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 Quantityq0 Price p1 Quantityq1 A 20 8 40 7 B 50 10 60 10 C 40 15 60 x D 12 15 15 15

#### 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?

#### 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