Find x if the Price Index Number by Simple Aggregate Method is 125 Commodity P Q R S T Base Year Price (in ₹) 10 8 12 24 18 Current Year Price (in ₹) 14 10 x 28 22 - Mathematics and Statistics

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

Commodity P Q R S T
Base Year Price (in ₹) 10 8 12 24 18
Current Year Price (in ₹) 14 10 x 28 22
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Solution

Commodity Base year price
(in ₹) p0
Current year price
(in ₹) p1
P 10 14
Q 8 10
R 12 x
S 24 28
T 18 22
Total 72 74 + x

From the table, `sum"p"_0` = 72, `sum"p"_1` = 74 + x

P01 = `(sum"p"_1)/(sum"p"_0) xx100`

125 = `(74 + x)/2 xx 100`

∴ `(74 + x)/72 = 125/100`

∴ 74 + x = `5/4 xx 72`

∴ x = 90 – 74

∴ x = 16

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Chapter 2.5: Index Numbers - Q.4

RELATED QUESTIONS

Complete the Correlation:

Price Index : Inflation :: ______ : Agricultural production


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Price Index and Quantity Index.


Quantity Index Number by Weighted Aggregate Method is given by ______.


Choose the correct alternative :

Value Index Number by Weighted Aggregate Method is given by


Fill in the blank :

Value Index Number by Simple Aggregate Method is given by _______.


Fill in the blank :

Price Index Number by Weighted Aggregate Method is given by _______.


State whether the following is True or False :

`(sum"p"_1)/(sum"p"_0) xx 100` is the price Index Number by Simple Aggregate Method.


Solve the following problem :

Find the Price Index Number using Simple Aggregate Method. Consider 1980 as base year.

Commodity Price in 1980 (in ₹) Price in 1985 (in ₹)
I 22 46
II 38 36
III 20 28
IV 18 44
V 12 16

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Choose the correct alternative:

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


Quantity Index Number by Weighted Aggregate Method is given by ______


Price Index Number by Weighted Aggregate Method is given by ______


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The three types of Index numbers are
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State whether the following statement is True or False:

`sum ("P"_1"q"_1)/("p"_0"q"_0) xx 100` is the Value Index Number by Simple Aggregate Method


Find Price Index Number using Simple Aggregate method by taking 2005 as base year.

Commodity P Q R S T
Price in 2005 (in ₹) 10 25 14 20 30
Price in 2015 (in ₹) 32 40 20 45 70

Calculate Quantity Index Number using Simple Aggregate method

Commodity I II III IV V
Base year Quantity 140 120 100 200 225
Current year Quantity 100 80 70 150 185

Find Price Index Number using Simple Aggregate method by taking 2000 as base year

Commodity Price (in ₹) for
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Price (in ₹) for
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Watch 900 1,475
Shoes 1,760 2,300
Sunglasses 60 1,040
Mobile 4,500 8,500

Find values x and y if the Price Index Number by Simple Aggregate Method by taking 2001 as base year is 120, given `sum"p"_1` = 300.

Commodity A B C D
Price (in ₹) in 2001 90 x 90 30
Price (in ₹) in 2004 95 60 y 35

Find x from following data if the Value Index Number is 200.

Commodity Base Year Current Year
Prive Quantity Price Quantity
A 10 10 20 10
B 8 20 22 15
C 2 x 8 10
D 9 10 16 10
E 5 6 3 10

Choose the correct pair:

Group A Group B
A. Price Index (a) `(sump_1q_1)/(sump_0q_0) xx 100`
B. Value Index (b) `(sumq_1)/(sumq_0) xx 100`
C. Quantity Index (c) `(sump_1q_1)/(sump_0q_1) xx 100`
D. Paasche's Index (d) `(sump_1)/(sump_0) xx 100`

The Price Index Number for year 2004, with respect to year 2000 as base year. is known to be 130. Find the missing numbers in the following table if ∑p0 = 320

Commodity A B C D E F
Price (in ₹) in 2000 40 50 30 x 60 100
Price (in ₹) in 2000 50 70 30 85 y 115

Choose the correct pair :

Group A Group B
1) Price Index a) `(sum p_1q_1)/(sum p_0q_0) xx 100`
2) Value Index b) `(sum q_1)/(sum q_0) xx 100`
3) Quantity Index c) `(sum p_1q_1)/(sum p_0 q_1) xx 100`
4) Paasche's Index d) `(sum p_1)/(sum p_0) xx 100`

Choose the correct pair:

Group A Group B
1) Price Index a) `(sump_1q_1)/(sump_0 q_0) × 100`
2) Value Index b) `(sumq_1)/(sumq_0) × 100`
3) Quantity Index c) `(sump_1q_1)/(sump_0 q_1) × 100`
4) Paasche's Index d) `(sump_1)/(sump_0) × 100`

Calculate the price index number for the given data.

Commodity A B
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Price in 2021 (₹) 40 40

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

The quantity index number is one type of index number.


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An index number measuring the general changes in the prices of goods over a period of time.


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Explain the meaning of the Price Index Number.


Identify and explain the concept from the given illustration:

Pooja collected information regarding a change in the quantity of imports of India from 2019 to 2020 and prepared an index number.


Choose the correct pair :

Group A Group B
1) Price Index a)

`(sump1q1)/(sump0q0)xx100`

2) Value Index b) `(sumq1)/(sumq0)xx100`
3) Quantity Index c) `(sump1q1)/(sump0q1)xx100`
4) Paasche's Index d) `(sump1)/(sump0)xx100`

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

There are many types of index numbers.


Observe the following table and answer the questions given below it:

Commodities Prices in 2006 (in ₹) (Base Year) P0 Prices in 2006 (in ₹) (Current Year) P1
A 20 30
B 30 45
C 40 60
D 50 75
E 60 90

Questions:

  1. Write the formula for calculation of price index.
  2. Find the value of ∑P0 and ∑P1.
  3. Find the price index P01.

Choose the correct pair :

  Group A   Group B
1) Price Index a) `(sump_1q_1)/(sump_0q_0) xx 100`
2) Value Index b) `(sumq_1)/(sumq_0) xx 100`
3) Quantity Index c) `(sump_1q_1)/(sump_0q_1) xx 100`
4) Paasche's Index d) `(sump_1)/(sump_0) xx 100`

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