SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.5 - Index Numbers [Latest edition]

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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.5 - Index Numbers - Shaalaa.com
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Solutions for Chapter 2.5: Index Numbers

Below listed, you can find solutions for Chapter 2.5 of Maharashtra State Board SCERT Maharashtra Question Bank for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022.


Q.1Q.2Q.3Q.4Q.5
Q.1

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.5 Index Numbers Q.1

MCQ [ Mark]

Q.1 | Q 1

Choose the correct alternative:

Price Index Number by using Weighted Aggregate Method is given by

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

  • `sum"p"_1"w" xx 100`

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

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

Q.1 | Q 2

Choose the correct alternative:

The formula P01 = `(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is for

  • Laspeyre’s Price Index Number

  • Paasche’s Price Index Number

  • Fisher’s Price Index Number

  • Walsh’s Price Index Number

Q.1 | Q 3

Choose the correct alternative:

Dorbish–Bowley’s Price Index Number is

  • P01(L) + P01(P)

  • P01(L) – P01(P)

  • `("P"_(01)("L") + "P"_(01)("P"))/2 xx 100`

  • `("P"_(01)("L") + "P"_(01)("P"))/2`

Q.1 | Q 4

Choose the correct alternative:

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

  • Value Index Number by Simple Aggregate method

  • Value Index Number by Weighted Aggregate method

  • Cost of Living Index Number

  • Laspeyre’s Index Number

Q.1 | Q 5

Choose the correct alternative:

Walsh's Price Index Number is given by

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

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

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

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

Q.1 | Q 6

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

  • `sum(q_1)/(q_0) xx 100`

  • `sum(q_0)/(q_1) xx 100`

  • `(sumq_1)/(sumq_0) xx 100`

  • `(sumq_0)/(sumq_1) xx 100`

Q.1 | Q 7

Choose the correct alternative:

Fisher’s Price Index Number is

  • `sqrt("P"_(01)("L") xx "P"_(01)("P"))`

  • P01(L) × P01(P)

  • `sqrt("P"_(01)("L") xx "P"_(01)("P")) xx 100`

  • `sqrt("P"_(01)("L") + "P"_(01)("P"))`

Q.1 | Q 8

Choose the correct alternative:

The Cost of Living Index Number using Weighted Relative Method is given by

  • `(sum"IW")/(sum"W") xx 100`

  • `(sum"IW")/(sum"W")`

  • `(sum"W")/(sum"IW") xx 100`

  • `(sum"W")/(sum"IW")`

Q.1 | Q 9

Choose the correct alternative: 

The Cost of Living Index Number by Aggregate Expenditure Method is same as

  • Fisher’s Price Index Number

  • Laspeyre’s Price Index Number

  • Paasche’s Price Index Number

  • Dorbish-Bowley’s Price Index Number

Q.2

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.5 Index Numbers Q.2

Fill in the blanks [1 Mark]

Q.2 | Q 1

Price Index Number by Simple Aggregate Method is given by ______

Q.2 | Q 2

Value Index Number by Simple Aggregate Method is given by ______

Q.2 | Q 3

Fisher's Price Index Number is given by ______.

Q.2 | Q 4

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

Q.2 | Q 5

The Cost of Living Index Number by Aggregate Expenditure Method is given by ______

Q.2 | Q 6

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

Q.2 | Q 7

Quantity Index Number by Weighted Aggregate Method is given by ______

Q.2 | Q 8

Price Index Number by Weighted Aggregate Method is given by ______

Q.3

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.5 Index Numbers Q.3

[1 Mark]

Q.3 | Q 1

State whether the following statement is True or False:

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

  • True

  • False

Q.3 | Q 2

State whether the following statement is True or False:

The three types of Index numbers are
i. Price Index Number
ii. Quantity Index Number
iii. Value Index Number

  • True

  • False

Q.3 | Q 3

State whether the following statement is True or False:

For Cost of Living Index Number CLI =`(sum"IW")/(sum"W")`, where I = `("P"_0)/("P"_1) xx 100` and w = p0q0

  • True

  • False

Q.3 | Q 4

State whether the following statement is True or False:

Purchasing power of money = `1/"Cost of Living Index Number"`

  • True

  • False

Q.3 | Q 5

State whether the following statement is True or False:

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

  • True

  • False

Q.3 | Q 6

State whether the following statement is True or False:

`(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100` is Paasche’s Price Index Number

  • True

  • False

Q.3 | Q 7

State whether the following statement is True or False:

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

  • True

  • False

Q.3 | Q 8

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.

  • True

  • False

Q.3 | Q 9

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

  • True

  • False

Q.4

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.5 Index Numbers Q.4

Solve the following problems [4 Marks]

Q.4 | Q 1

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
Q.4 | Q 2

Find Quantity Index Number using Simple Aggregate method

Commodity A B C D E
Base year Quantity 170 150 100 195 205
Current year Quantity 90 70 75 150 95
Q.4 | Q 3

Calculate Value Index Number for the following using Simple Aggregate Method

Commodity Base Year Current Year
Price Quantity Price  Quantity
A 30 13 40 15
B 40 15 70 20
C 10 12 60 22
D 50 10 90 18
E 20 14 100 16
Q.4 | Q 4

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
Q.4 | Q 5

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

Commodity Price (in ₹) for
year 2000
Price (in ₹) for
year 2007
Watch 900 1,475
Shoes 1,760 2,300
Sunglasses 60 1,040
Mobile 4,500 8,500
Q.4 | Q 6

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
Q.4 | Q 7

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
Q.4 | Q 8

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
Q.4 | Q 9

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
Q.4 | Q 10

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
Q.4 | Q 11

Calculate Walsh’s price Index Number for the following data.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 12 40 3
II 20 2 25 8
III 30 3 50 27
IV 60 9 90 36
Q.4 | Q 12

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

Q.4 | Q 13

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

Q.4 | Q 14

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)

Q.4 | Q 15

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
Q.4 | Q 16

If `sum"p"_0"q"_0` = 150, `sum"p"_0"q"_1` = 250, `sum"p"_1"q"_1` = 375 and P01(L) = 140. Find P01(M-E)

Q.4 | Q 17

Calculate the Cost of Living Index Number for the following data.

Group Base Year Current Year
Price Quantity Price
Food 40 5 20
Clothing 30 10 35
Fuel and Lighting 20 17 10
House Rent 60 22 10
Miscellaneous 70 25 8
Q.4 | Q 18

Calculate the Cost of Living Index by Family Budget method in following example where W are wages of base year and I are current year price relatives.

Group Food Clothing Fuel and
Lighting
House
Rent
Miscellaneous
I 150 140 100 120 200
W 4 3 3 4 6
Q.4 | Q 19

Find the missing wage if the Cost of Living Index for the following data is 150.

Group Food Clothing Fuel and
Lighting
House
Rent
Miscellaneous
I 200 150 140 100 120
W 6 4 x 3 4
Q.4 | Q 20

The Cost of Living Index Numbers for years 2003 and 2008 are 150 and 200 respectively. A person earned ₹ 18,000 per month in year 2003. What should be his earning per month in year 2008, so as to maintain same standard of living as 2003?

Q.5

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.5 Index Numbers Q.5

Activity [4 Marks]

Q.5 | Q 1

Given the following table, find Walsh’s Price Index Number by completing the activity.

Commodity p0 q0 p1 q1 q0q1 `sqrt("q"_0"q"_1)` p0`sqrt("q"_0"q"_1)` p1`sqrt("q"_0"q"_1)`
I 20 9 30 4 36 `square` `square` 180
II 10 5 50 5 `square` 5 50 `square`
III 40 8 10 2 16 `square` 160 `square`
IV 30 4 20 1 `square` 2 `square` 40
Total     390 `square`

Walsh’s price Index Number is

P01(W) = `square/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

= `510/square xx 100`

= `square`

Q.5 | Q 2

Given the following table, find the Cost of living Index Number using Aggregate Expenditure Method by completing the activity.

Group p0 q0 p1 p0q0 p1q0
A 23 4 25 `square` 100
B 15 5 20 75 `square`
C 5 9 8 `square` 72
D 12 5 18 60 `square`
E 8 6 13 `square` 78
Total 320 `square`

Therefore, Cost of Living Index using Aggregate Expenditure method is

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

= `square/square xx 100`

= `square`

Solutions for Chapter 2.5: Index Numbers

Q.1Q.2Q.3Q.4Q.5
SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.5 - Index Numbers - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.5 - Index Numbers

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.5 Index Numbers are Index Numbers, Types of Index Numbers, Index Numbers - Terminology and Notation, Construction of Index Numbers, Simple Aggregate Method, Weighted Aggregate Method, Cost of Living Index Number, Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method, Method of Constructing Cost of Living Index Numbers - Family Budget Method, Uses of Cost of Living Index Number.

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