हिंदी

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 Quantityq0 Pricep1 Quantityq1 A 3 x 2 5 B 4 6 3 5

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प्रश्न

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
सारिणी
योग
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उत्तर

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 = 24 + 3x = 35 = 18 + 2x  = 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.

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Construction of Index Numbers - Weighted Aggregate Method
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Index Numbers - Miscellaneous Exercise 5 [पृष्ठ ९३]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 5 Index Numbers
Miscellaneous Exercise 5 | Q 4.1 | पृष्ठ ९३

संबंधित प्रश्न

Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and MarshallEdgeworth’s Price index numbers.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 8 20 11 15
B 7 10 12 10
C 3 30 5 25
D 2 50 4 35

Calculate Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall - Edgeworth’s Price index numbers.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 9 20 8
II 20 5 30 4
III 30 7 50 5
IV 40 8 60 6

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
L 4 16 3 19
M 6 16 8 14
N 8 28 7 32

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 12 20 9
II 20 4 25 8
III 30 13 40 27
IV 60 29 75 36

If ∑p0q0 = 140, ∑p0q1 = 200, ∑p1q0 = 350, ∑p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.


Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.


Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.

Commodity Base Year Current year
Price Quantity Price Quantity
A 2 10 2 5
B 2 5 x 2

Dorbish-Bowley’s Price Index Number is given by ______.


Choose the correct alternative :

Fisher’s Price Number is given by


Choose the correct alternative :

Marshall-Edgeworth’s Price Index Number is given by


Choose the correct alternative :

Walsh’s Price Index Number is given by


Fill in the blank :

Paasche’s Price Index Number is given by _______.


`(sump_1q_0)/(sump_0q_0) xx 100` is Paasche’s Price Index Number.


State whether the following is True or False :

`sqrt(("p"_1"q"_0)/(sum"p"_0"q"_0)) xx sqrt((sum"p"_1"q"_1)/(sum"p"_0"q"_1)) xx 100` is Fisher’s Price Index Number.


Solve the following problem :

Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.

Commodity Base year Current year
  Price
p0
Quantity
q0
price
p1
Quantity
q1
A 20 18 30 15
B 25 8 28 5
C 32 5 40 7
D 12 10 18 10

Calculate Walsh’s Price Index Number for the following data.

Commodity Base year Current year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
I 8 30 12 25
II 10 42 20 16

Solve the following problem:

If find x is Walsh’s Price Index Number is 150 for the following data

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
A 5 3 10 3
B x 4 16 9
C 15 5 23 5
D 10 2 26 8

Solve the following problem :

Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.


Choose the correct alternative:

The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for


Choose the correct alternative:

Fisher’s Price Index Number is


State whether the following statement is True or False:

Walsh’s Price Index Number is given by `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`


State whether the following statement is True or False:

`(sum"p"_0sqrt("q"_0 + "q"_1))/(sum"p"_1sqrt("q"_0 + "q"_1)) xx 100` is Marshall-Edgeworth Price Index Number


State whether the following statement is true or false:

Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.


Laspeyre’s Price Index Number uses current year’s quantities as weights.


Calculate Marshall – Edgeworth’s price index number for the following data:

Commodity Base year Current year
Price Quantity Price Quantity
P 12 20 18 24
Q 14 12 21 16
R 8 10 12 18
S 16 15 20 25

If ∑ p0q0 = 120, ∑ p0q1 = 160, ∑ p1q1 = 140, ∑ p1qo = 200, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.


Complete the following activity to calculate, Laspeyre's and Paasche's Price Index Number for the following data :

Commodity Base Year Current Year
Price
p0
Quantity
q0
Price
p1
Quantity
q1
I 8 30 12 25
II 10 42 20 16

Solution:

Commodity Base Year Current Year p1q0 p0q0 p1q1 p0q1
  p0 q0 p1 q1
I 8 30 12 25 360 240 300 200
II 10 42 20 16 840 420 320 160
Total         `bb(sump_1q_0=1200)` `bb(sump_0q_0=660)` `bb(sump_1q_1=620)` `bb(sump_0q_1=360)`

Laspeyre's Price Index Number:

P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100 = square/660xx100`

∴ P01(L) = `square`

Paasche 's Price Index Number:

P01(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100=(620)/(square) xx 100`

∴ P01(P) = `square`


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