Given P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P01(L)

Given, P01(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320 P01(M-E) = `(sum"p"_1"q"_0 + sum"p"_1"q"_1)/(sum"p"_0"q"_0 + sum"p"_0"q"_1) xx 100` &there4; 120 = `(sum"p"_1"q"_0 + 300)/(120 + 130) xx 100` &there4; 120 = `(sum"p"_1"q"_0 + 300)/440 xx 100` &there4; `sum"p"_1"q"_0 + 300 = (120 xx 440)/100` &there4; `sum"p"_1"q"_0 + 300` = 528 &there4; `sum"p"_1"q"_0` = 528 – 300 &there4; `sum"p"_1"q"_0` = 228 Laspeyre’s Price Index Number: P01(L) = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` = `228/120 xx 100` = 190

Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

प्रश्न

Given P₀₁(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320, Find P₀₁(L)

बेरीज

उत्तर

Given, P₀₁(M-E) = 120, `sum"p"_1"q"_1` = 300, `sum"p"_0"q"_0` = 120, `sum"p"_0"q"_1` = 320

P₀₁(M-E) = `(sum"p"_1"q"_0 + sum"p"_1"q"_1)/(sum"p"_0"q"_0 + sum"p"_0"q"_1) xx 100`

∴ 120 = `(sum"p"_1"q"_0 + 300)/(120 + 130) xx 100`

∴ 120 = `(sum"p"_1"q"_0 + 300)/440 xx 100`

∴ `sum"p"_1"q"_0 + 300 = (120 xx 440)/100`

∴ `sum"p"_1"q"_0 + 300` = 528

∴ `sum"p"_1"q"_0` = 528 – 300

∴ `sum"p"_1"q"_0` = 228

Laspeyre’s Price Index Number:

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

= `228/120 xx 100`

= 190

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Construction of Index Numbers - Weighted Aggregate Method

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पाठ 2.5: Index Numbers - Q.4

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एससीईआरटी महाराष्ट्र Mathematics and Statistics (Commerce) [English] Standard 12 Maharashtra State Board

पाठ 2.5 Index Numbers
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2021-2022 (March) Model set 3 shaalaa.com (with solutions)

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संबंधित प्रश्‍न

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

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

Commodity	Base Year		Current Year
Commodity	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
Commodity	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).

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.

Paasche’s Price Index Number is given by ______.

Fill in the blank :

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Walsh’s Price Index Number is given by _______.

`(sump_1q_0)/(sump_0q_0) xx 100` is Paasche’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.

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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

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:

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

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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

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

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Commodity	Base Year		Current Year
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A	10	9	50	8
B	20	5	60	4
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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
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Commodity	Base Year		Current Year
Commodity	Price	Quantity	Price	Quantity
A	1	10	2	5
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If P₀₁ (L) = 121, P₀₁ (P) = 100, then P₀₁ (F) = ______.

Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

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Given P01(M-E) = 120, ∑p1q1 = 300, ∑p0q0 = 120, ∑p0q1 = 320, Find P01(L)

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