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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data. Commodity Base Year Current Year Price Quantity Price Quantity A 1 10 2 5 B 1 5 – 12 - Mathematics and Statistics

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प्रश्न

Find the missing price if Laspeyre’s and Paasche’s Price Index Numbers are equal for following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 1 10 2 5
B 1 12
तक्ता
बेरीज
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उत्तर

Let us denote the missing value by x and reconstruct the table as follows.

Commodity Base Year Current Year p0q0 p1q0 p1q1 p0q1
p0 q0 p1 q1
A 1 10 2 5 10 20 10 5
B 1 5 x 12 5 5x 1 12
Total         15 20 + 5x 10 + 12x 17

The above table gives

`sum"p"0"q"_0` = 15, `sum"p"_1"q"_0` = 20  5x, `sum"p"_1"q"_1` = 10 + 12x, `sum"p"_0"q"_1` = 17

It is given that

P01(L) = P01(P)

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

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

∴ `(5x + 20)/15 = (12x + 10)/17`

∴ `(5(x + 4))/15 = (12x + 10)/17`

∴ 17(x + 4) = 3(12x + 10)

∴ 17x + 68 = 36x + 30

∴ x = 2

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Construction of Index Numbers - Weighted Aggregate Method
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पाठ 2.5: Index Numbers - Q.4

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 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 P01(L) = 90 and P01(P) = 40, find P01(D – B) and P01(F).


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

Choose the correct alternative :

The price Index Number by Weighted Aggregate Method is given by ______.


Laspeyre’s Price Index Number is given by ______.


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


Laspeyre’s Price Index Number is given by _______.


Fill in the blank :

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


Fill in the blank :

Marshall-Edgeworth’s Price Index Number is given by _______.


State whether the following is True or False :

`sum("p"_1"q"_1)/("p"_0"q"_1)` is Laspeyre’s Price Index Number.


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


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 :

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

Solve the following problem :

If `sum"p_"0"q"_0 = 120, sum "p"_0"q"_1 = 160, sum "p"_1"q"_1 = 140, and sum "p"_1"q"+0` = 200, find Laspeyre’s, Paasche’s Dorbish-Bowley’s and Marshall Edgeworth’s Price Index Number.


Solve the following problem :

Given that `sum "p"_0"q"_0 = 130, sum "p"_1"q"_1 = 140, sum "p"_0"q"_1 = 160, and sum "p"_1"q"_0 = 200`, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.


The average of Laspeyre’s and Paasche’s Price Index Numbers is called ______ Price Index Number


State whether the following statement is True or False:

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


Calculate
a) Laspeyre’s
b) Passche’s
c) Dorbish-Bowley’s Price Index Numbers for following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 10 9 50 8
B 20 5 60 4
C 30 7 70 3
D 40 8 80 2

Calculate Marshall-Edgeworth Price Index Number for following.

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

If P01(L) = 40 and P01(P) = 90, find P01(D-B) and P01(F).


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.


If P01 (L) = 121, P01 (P) = 100, then P01 (F) = ______.


`sqrt((sump_1q_0)/(sump_0q_0)) xx sqrt((sump_1q_1)/(sump_0q_1)) xx 100`


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

In the following table, Laspeyre's and Paasche's Price Index Numbers are equal. Complete the following activity to find x :

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

Solution: P01(L) = P01(P)

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

`(20 + 5x)/square xx 100 = square/14 xx 100`

∴ x = `square`


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