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Maharashtra State BoardHSC Commerce (English Medium) 12th Standard Board Exam

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∑p1q0∑p0q0×∑p1q1∑p0q1×100 - Mathematics and Statistics

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Question

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

Options

True
False

MCQ

True or False

Solution

This statement is False.

shaalaa.com

Construction of Index Numbers - Weighted Aggregate Method

Is there an error in this question or solution?

Q 4.B.iii Q 4.B.ii Q 4.C.i

2024-2025 (March) Model set 1 by shaalaa.com

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2024-2025 (March) Model set 1 by shaalaa.com (with solutions)

Q 4.B.iii | 1 mark

RELATED QUESTIONS

Calculate Walsh’s Price Index Number.

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

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
Commodity	Price	Quantity	Price	Quantity
A	2	10	2	5
B	2	5	x	2

If Laspeyre's Price Index Number is four times Paasche's Price Index Number, then find the relation between Dorbish-Bowley's and Fisher's Price Index Numbers.

Laspeyre’s Price Index Number is given by ______.

Paasche’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

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 Dorbish-Bowley’s Price Index Number for the following data.

Commodity	Base Year		Current Year
	Price p₀	Quantity q₀	Price p₁	Quantity q₁
I	8	30	11	28
II	9	25	12	22
III	10	15	13	11

Solve the following problem :

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 :

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

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

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.

Choose the correct alternative:

Walsh's Price Index Number is given by

Marshall-Edgeworth's Price Index Number is given by ______

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
Commodity	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
Commodity	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 for the following data.

Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
I	10	12	40	3
II	20	2	25	8
III	30	3	50	27
IV	60	9	90	36

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

If Laspeyre’s and Paasche’s Price Index Numbers are 50 and 72 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Numbers

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

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

Commodity	Base Year		Current Year
Commodity	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	p₁q₀	p₀q₀	p₁q₁	p₀q₁
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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