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

Find x if the Price Index Number by Simple Aggregate Method is 120, taking 1995 as base year. - Mathematics and Statistics

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प्रश्न

Find x if the Price Index Number by Simple Aggregate Method is 120, taking 1995 as base year.

Commodity A B C D
Price (in ₹) for 1995 95 y 80 35
Price (in ₹) for 2003 116 74 92 42
बेरीज

उत्तर

Commodity Price in 1995
(Base year) 
Price in 2003 (Current year)
p0 p1
A 95 116
B y 74
C 80 92
D 35 42
Total y + 210 324

From the table, `sum "p"_0 = y + 210, sum "p"_1 = 324`

Given, Price Index Number (P01) = 120

Since `"P"_01 = (sum "p"_1)/(sum "p"_0) xx 100`

`120 = 324/("y" + 210) xx 100`

∴ y + 210 = `(324 xx 100)/120`

∴ y + 210 = 270

∴  y = 60

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पाठ 5: Index Numbers - Exercise 5.1 [पृष्ठ ७८]

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संबंधित प्रश्‍न

Laaspeyre's index : _________ :: Paasche's index : Current year quantities


Solve the following:

Calculate Quantity Index number from the given data:

Commodity P Q R S T
Base year quantities 170 150 100 195 205
Current year quantities 90 70 75 150 95

Solve the following:

Calculate Paasche's index from the given data:

Commodity Base year current year
Price Quantity Price Quantity
X 8 30 12 25
Y 10 42 20 16

Explain the steps involved in the construction of index numbers.


Find the Price Index Number using Simple Aggregate Method in the following example.

Use 1995 as base year in the following problem.

Commodity P Q R S T
Price (in ₹) in 1995 15 20 24 23 28
Price (in ₹) in 2000 27 38 32 40 45

Find the Price Index Number using Simple Aggregate Method in the following example.

Use 1995 as base year in the following problem.

Commodity A B C D E
Price (in ₹) in 1995 42 30 54 70 120
Price (in ₹) in 2005 60 55 74 110 140

Find the Price Index Number using the Simple Aggregate Method in the following example.

Use 2000 as base year in the following problem.

Commodity Price (in ₹) for
year 2000
Price (in ₹) for year 2006
Watch 900 1475
Shoes 1760 2300
Sunglasses 600 1040
Mobile 4500 8500

Find the Price Index Number using the Simple Aggregate Method in the following example.

Assume 2000 to be base year in the following problem.

Fruit Unit Price (in ₹)  
in 2000
Price
(in ₹) for 2007
Mango doz 250 300
Banana doz 12 24
Apple kg 80 110
Peach kg 75 90
Orange doz 36 65
Sweet Lime doz 30 45

Find the Quantity Index Number using the Simple Aggregate Method in the following example.

Commodity A B C D E
Base Year Quantities 360 280 340 160 260
Current Year Quantities 440 320 470 210 300

Find the Value Index Number using Simple Aggregate Method in the following example.

Commodity Base Year Current Year
Price Quantity Price Quantity
A 50 22 70 14
B 70 16 90 22
C 60 18 105 14
D 120 12 140 15
E 100 22 155 28

Find x if the Price Index Number by Simple Aggregate Method is 125.

Commodity P Q R S T
Base Year Price (in ₹) 8 12 16 22 18
Current Year
Price (in ₹)
12 18 x 28 22

Statements related to weighted index number:

  1. Suitable weights are assigned to various commodities.
  2. It gives relative importance to the commodity in the group.
  3. In most cases, quantities are used as weights.
  4. Laaspeyre’s Price index and Paasche’s Price Index are methods of constructing weighted index number.

Find the odd word

Steps involved in the construction of index number -


Assertion (A): Generally, arithmetic mean is used in the construction of index numbers.

Reasoning (R): Arithmetic mean is simple to compute compared to other averages.


State with reason whether you agree or disagree with the following statement:

Any year can be selected as the base year


State with reasons whether you agree or disagree with the following statement:

It is not essential to decide the purpose of an index number while constructing it.


Explain the steps in constructing a price index number.


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