Maharashtra State BoardHSC Commerce 12th Board Exam
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Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 5 - Index Numbers [Latest edition]

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Chapters

Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Chapter 5: Index Numbers

Exercise 5.1Exercise 5.2Exercise 5.3Miscellaneous Exercise 5
Exercise 5.1 [Pages 77 - 78]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 5 Index Numbers Exercise 5.1 [Pages 77 - 78]

Exercise 5.1 | Q 1.01 | Page 77

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 22 28
Price (in ₹) in 2000 27 38 32 40 45
Exercise 5.1 | Q 1.02 | Page 77

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
Exercise 5.1 | Q 1.03 | Page 77

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

Commodity Unit Base Year Price (in ₹) Current Year Price
(in ₹)
Wheat kg 28 36
Rice kg 40 56
Milk litre 35 45
Clothing meter 82 104
Fuel litre 58 72
Exercise 5.1 | Q 1.04 | Page 77

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
Exercise 5.1 | Q 1.05 | Page 77

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

Use 1990 as base year in the following problem.

Commodity Unit Price (in ₹) for
year 2000
Price (in ₹) for year 2006
Butter kg 27 33
Cheese kg 30 36
Milk litre 25 29
Bread loaf 10 14
Eggs doz 24 36
Ghee tin 250 320
Exercise 5.1 | Q 1.06 | Page 78

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
Exercise 5.1 | Q 1.07 | Page 78

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

Use 2005 as base year in the following problem.

Vegetable Unit Price (in ₹)  
in 2005
Price
(in ₹) for 2012
Ladies Finger kg 32 38
Capsicum kg 30 36
Brinjal kg 40 60
Tomato kg 40 62
Potato kg 16 28
Exercise 5.1 | Q 1.08 | Page 78

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

Commodity I II III IV V
Base Year Quantities 140 120 100 200 225
Current Year Quantities 100 80 70 150 185
Exercise 5.1 | Q 1.09 | Page 78

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
Exercise 5.1 | Q 1.1 | Page 78

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

 

Commodity Base Year Current Year
Price Quantity Price Quantity
A 30 22 40 18
B 40 16 60 12
C 10 38 15 24
D 50 12 60 16
E 20 28 25 36
Exercise 5.1 | Q 1.11 | Page 78

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
Exercise 5.1 | Q 1.12 | Page 78

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
Exercise 5.1 | Q 1.13 | Page 78

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
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Exercise 5.2 [Page 82]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 5 Index Numbers Exercise 5.2 [Page 82]

Exercise 5.2 | Q 1.01 | Page 82

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

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
Exercise 5.2 | Q 1.02 | Page 82

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

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 9 20 8
II 20 5 30 4
III 30 7 50 5
IV 40 8 60 6
Exercise 5.2 | Q 1.03 | Page 82

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
L 4 16 3 19
M 6 16 8 14
N 8 28 7 32
Exercise 5.2 | Q 1.04 | Page 82

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 12 20 9
II 20 4 25 8
III 30 13 40 27
IV 60 29 75 36
Exercise 5.2 | Q 1.05 | Page 82

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

Exercise 5.2 | Q 1.06 | Page 82

If ∑ p0q0 = 140, ∑ p0q1 = 200, ∑ p1q0 = 350, ∑ p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.

Exercise 5.2 | Q 1.07 | Page 82

Given that Laspeyre’s and Dorbish-Bowley’s Price Index Numbers are 160.32 and 164.18 respectively, find Paasche’s Price Index Number.

Exercise 5.2 | Q 1.08 | Page 82

Given that ∑ p0q0 = 220, ∑ p0q1 = 380, ∑ p1q1 = 350 and MarshallEdgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.

Exercise 5.2 | Q 1.09 | Page 82

Find x in the following table if Laspeyre’s and Paasche’s Price Index Numbers are equal.

Commodity Base Year Current year
Price Quantity Price Quantity
A 2 10 2 5
B 2 5 x 2
Exercise 5.2 | Q 1.1 | Page 82

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.

Exercise 5.2 | Q 1.11 | Page 82

If Dorbish-Bowley's and Fisher's Price Index Numbers are 5 and 4, respectively, then find Laspeyre's and Paasche's Price Index Numbers.

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Exercise 5.3 [Page 87]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 5 Index Numbers Exercise 5.3 [Page 87]

Exercise 5.3 | Q 1 | Page 87

Calculate the cost of living index in problem 

Group Base Year Current Year
  Price Quantity Price
Food 120 15 170
Clothing 150 20 190
Fuel & Lighting 130 30 220
House Rent 160 10 180
Miscellaneous 200 12 200
Exercise 5.3 | Q 2 | Page 87

Calculate the cost of living index in problem

Group Base Year Current Year
  Price Quantity Price
Food 40 15 45
Clothing 30 10 35
Fuel & Lighting 20 17 25
House Rent 60 22 70
Miscellaneous 70 25 80
Exercise 5.3 | Q 3 | Page 87

Calculate the cost of living index in problem

Group Base Year Current Year
  Price Quantity Price
Food 132 10 170
Clothing 154 12 160
Fuel & Lighting 164 20 180
House Rent 175 18 195
Miscellaneous 128 5 120
Exercise 5.3 | Q 4 | Page 87

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 70 90 100 60 80
W 5 3 2 4 6
Exercise 5.3 | Q 5 | Page 87

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 400 300 150 120 100
W 3 3 4 5 2
Exercise 5.3 | Q 6 | Page 87

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 200 150 120 180 160
W 30 20 10 40 50
Exercise 5.3 | Q 7 | Page 87

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Find x if the cost of living index is 150.

Group Food Clothing Fuel & Lighting House Rent  Miscellaneous
I 180 120 300 100 160
W 4 5 6 x 3
Exercise 5.3 | Q 8 | Page 87

Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in:

Find y if the cost of living index is 200.

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 180 120 160 300 200
W 4 5 3 y 2
Exercise 5.3 | Q 9 | Page 87

The Cost of Living Index Number for years 1995 and 1999 are 140 and 200 respectively. A person earns ₹ 11,200 per month in the year 1995. What should be his monthly earnings in the year 1999 in order to maintain his standard of living as in the year 1995?

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Miscellaneous Exercise 5 [Pages 89 - 94]

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 5 Index Numbers Miscellaneous Exercise 5 [Pages 89 - 94]

Miscellaneous Exercise 5 | Q 1.01 | Page 89

Choose the correct alternative :

Price Index Number by Simple Aggregate Method is given by

  • `sum  "p"_1/"p"_0 xx 100`

  • `sum  "p"_0/"p"_1 xx 100`

  • `(sum  "p"_1)/(sum"p"_0) xx 100`

  • `(sum  "p"_0)/(sum"p"_1) xx 100`

Miscellaneous Exercise 5 | Q 1.02 | Page 89

Choose the correct alternative :

Quantity Index Number by Simple Aggregate Method is given by

  • `sum "q"_1/"q"_0 xx 100`

  • `sum "q"_0/"q"_1 xx 100`

  • `(sum "q"_1)/(sum"q"_0) xx 100`

  • `(sum "q"_1)/(sum"q"_0) xx 100`

Miscellaneous Exercise 5 | Q 1.03 | Page 90

Choose the correct alternative :

Value Index Number by Simple Aggregate Method is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.04 | Page 89

Choose the correct alternative :

Price Index Number by Weighted Aggregate Method is given by

  • `sum("p"_1"w")/("p"_0"w") xx 100`

  • `sum("p"_0"w")/("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`

Miscellaneous Exercise 5 | Q 1.05 | Page 89

Choose the correct alternative :

Quantity Index Number by Weighted Aggregate Method is given by

  • `sum("q"_1"w")/("q"_0"w") xx 100`

  • `sum("q"_0"w")/("q"_1"w") xx 100`

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

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

Miscellaneous Exercise 5 | Q 1.06 | Page 90

Choose the correct alternative :

Value Index Number by Weighted Aggregate Method is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.07 | Page 90

Choose the correct alternative :

Laspeyre’s Price Index Number is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.08 | Page 90

Choose the correct alternative :

Paasche’s Price Index Number is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.09 | Page 90

Choose the correct alternative :

Dorbish-Bowley’s Price Index Number is given by

  • `((sum"p"_1"q"_0)/(sum"p"_0"q"_1) + (sum"p"_0"q"_1)/(sum"p"_1"q"_0))/(2) xx 100`

  • `((sum"p"_1"q"_1)/(sum"p"_0"q"_0) + (sum"p"_0"q"_0)/(sum"p"_1"q"_1))/(2) xx 100`

  • `((sum"p"_1"q"_0)/(sum"p"_0"q"_0) + (sum"p"_1"q"_1)/(sum"p"_0"q"_1))/(2) xx 100`

  • `((sum"p"_0"q"_0)/(sum"p"_1"q"_0) + (sum"p"_0"q"_1)/(sum"p"_1"q"_1))/(2) xx 100`

Miscellaneous Exercise 5 | Q 1.1 | Page 90

Choose the correct alternative :

Fisher’s Price Number is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.11 | Page 90

Choose the correct alternative :

Marshall-Edgeworth’s Price Index Number is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.12 | Page 90

Choose the correct alternative :

Walsh’s Price Index Number is given by

  • `(sum"p"_1sqrt("q"_0"q"_1))/(sum"p"_0sqrt("q"_0"q"_1)) xx 100`

  • `(sum"p"_0sqrt("q"_0"q"_1))/(sum"p"_1sqrt("q"_0"q"_1)) xx 100`

  • `(sum"q"_1sqrt("p"_0"p"_1))/(sum"q"_0sqrt("p"_0"p"_1)) xx 100`

  • `(sum"q"_0sqrt("p"_0"p"_1))/(sum"q"_1sqrt("p"_0"p"_1)) xx 100`

Miscellaneous Exercise 5 | Q 1.13 | Page 91

Choose the correct alternative :

The cost of Living Index Number using Aggregate Expenditure Method is given by

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

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

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

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

Miscellaneous Exercise 5 | Q 1.14 | Page 91

Choose the correct alternative :

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

  • `(sum"IW")/(sum"W")`

  • `sum"W"/"IW"`

  • `(sum"W")/(sum"IW")`

  • `sum"IW"/"W"`

Miscellaneous Exercise 5 | Q 2.01 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.02 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.03 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.04 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.05 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.06 | Page 91

Fill in the blank :

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

Miscellaneous Exercise 5 | Q 2.07 | Page 91

Fill in the blank :

Laspeyre’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 2.08 | Page 91

Fill in the blank :

Paasche’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 2.09 | Page 91

Fill in the blank :

Dorbish-Bowley’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 2.1 | Page 91

Fill in the blank :

Fisher’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 2.11 | Page 91

Fill in the blank :

Marshall-Edgeworth’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 2.12 | Page 91

Fill in the blank :

Walsh’s Price Index Number is given by _______.

Miscellaneous Exercise 5 | Q 3.01 | Page 91

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.

  • True

  • False

Miscellaneous Exercise 5 | Q 3.02 | Page 91

State whether the following is True or False :

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

  • True

  • False

Miscellaneous Exercise 5 | Q 3.03 | Page 91

State whether the following is True or False :

`sum ("p"_0"q"_0)/("p"_1"q"_1)` is Value Index Number by Simple Aggregate Method.

  • True

  • False

Miscellaneous Exercise 5 | Q 3.04 | Page 91

State whether the following is True or False :

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

  • True

  • False

Miscellaneous Exercise 5 | Q 3.05 | Page 91

State whether the following is True or False :

`sum("p"_1"q"_1)/("p"_0"q"_1)` is Laspeyre’s Price Index Number.

  • True

  • False

Miscellaneous Exercise 5 | Q 3.06 | Page 92

State whether the following is True or False :

`(sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx (sum"p"_1"q"_0)/(sum"p"_0"q"_0) xx 100` is Dorbish-Bowley’s Price Index Number.

  • True

  • False

Miscellaneous Exercise 5 | Q 3.07 | Page 92

State whether the following is True or False :

`(1)/(2)[sqrt((sum"p"_1"q"_0)/(sum"p"_0"q"_0)) + sqrt("p"_1"q"_1)/(sqrt("p"_0"q"_1))] xx 100` is Fisher’s Price Index Number.

  • True

  • False

Miscellaneous Exercise 5 | Q 3.08 | Page 92

State whether the following is True or False :

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

  • True

  • False

Miscellaneous Exercise 5 | Q 3.09 | Page 92

State whether the following is True or False :

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

  • True

  • False

Miscellaneous Exercise 5 | Q 3.1 | Page 92

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.

  • True

  • False

Miscellaneous Exercise 5 | Q 4.01 | Page 92

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
Miscellaneous Exercise 5 | Q 4.02 | Page 92

Solve the following problem :

Find the Quantity Index Number using Simple Aggregate Method.

Commodity Base year quantity Current year quantity
A 100 130
B 170 200
C 210 250
D 90 110
E 50 150
Miscellaneous Exercise 5 | Q 4.03 | Page 92

Solve the following problem :

Find the Value Index Number using Simple Aggregate Method.

Commodity Base Year Current Year
  Price Quantity Price Quantity
I 20 42 22 45
II 35 60 40 58
III 50 22 55 24
IV 60 56 70 62
V 25 40 30 41
Miscellaneous Exercise 5 | Q 4.04 | Page 92

Solve the following problem :

Find x if the Price Index Number using Simple Aggregate Method is 200.

Commodity P Q R S T
Base Year Price 20 12 22 23 13
Current Year Price 30 x 38 51 19
Miscellaneous Exercise 5 | Q 4.05 | Page 92

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
A 20 18 30 15
B 25 8 28 5
C 32 5 40 7
D 12 10 18 10
Miscellaneous Exercise 5 | Q 4.06 | Page 92

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
Miscellaneous Exercise 5 | Q 4.07 | Page 92

Solve the following problem :

Calculate Marshall-Edgeworth’s Price Index Number for the following data.

Commodity Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Quantity
q1
X 12 35 15 25
Y 29 50 30 70
Miscellaneous Exercise 5 | Q 4.08 | Page 93

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
Miscellaneous Exercise 5 | Q 4.09 | Page 93

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
Miscellaneous Exercise 5 | Q 4.1 | Page 93

Solve the following problem : 

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
Miscellaneous Exercise 5 | Q 4.11 | Page 93

Solve the following problem :

Find x if 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
Miscellaneous Exercise 5 | Q 4.12 | Page 93

Solve the following problem :

Find x if Paasche’s Price Index Number is 140 for the following data.

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
Miscellaneous Exercise 5 | Q 4.13 | Page 93

Solve the following problem :

Given that Laspeyre’s and Paasche’s Price Index Numbers are 25 and 16 respectively, find Dorbish-Bowley’s and Fisher’s Price Index Number.

Miscellaneous Exercise 5 | Q 4.14 | Page 93

Solve the following problem :

If Laspeyre’s and Dorbish’s Price Index Numbers are 150.2 and 152.8 respectively, find Paasche’s Price Index Number.

Miscellaneous Exercise 5 | Q 4.15 | Page 93

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.

Miscellaneous Exercise 5 | Q 4.16 | Page 93

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.

Miscellaneous Exercise 5 | Q 4.17 | Page 93

Solve the following problem :

Given that `sum "p"_1"q"_1 = 300, sum "p"_0"q"_1 = 320, sum "p"_0"q"_0` = 120, and Marshall- Edgeworth’s Price Index Number is 120, find `sum"p"_1"q"_0` and Paasche’s Price Index Number.

Miscellaneous Exercise 5 | Q 4.18 | Page 93

Solve the following problem :

Calculate the cost of living number for the following data.

Group Base Year Current Year
  Price
p0
Quantity
q0
Price
p1
Food 150 13 160
Clothing 170 18 150
Fuel and Lighting 175 10 190
House Rent 200 12 210
Miscellaneous 210 15 260
Miscellaneous Exercise 5 | Q 4.19 | Page 94

Solve the following problem :

Find the cost living index number by the Weighted Aggregate Method.

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 78 80 110 60 90
W 5 3 4 2 6
Miscellaneous Exercise 5 | Q 4.2 | Page 94

Solve the following problem :

Find the cost of living index number by Family Budget Method for the following data. Also, find the expenditure of a person in the year 2008 if his expenditure in the year 2005 was ₹ 10,000.

Group Base Year
(2005) Price
Current Year
(2008) Price
Weight
Food 12 60 25
Clothing 10 45 20
Fuel and Lighting 20 35 15
House Rent 25 20 30
Miscellaneous 16 48 10
Miscellaneous Exercise 5 | Q 4.21 | Page 94

Solve the following problem :

Find x if the cost of living index number is 193 for the following data.

Group Food Clothing Fuel & Lighting House Rent Miscellaneous
I 221 198 171 183 161
W 35 14 x 8 20
Miscellaneous Exercise 5 | Q 4.22 | Page 94

Solve the following problem :

The cost of living index number for year 2000 and 2003 are 150 and 210 respectively. A person earns ₹ 13,500 per month in the year 2000. What should be his monthly earning in the year 2003 in order to maintain the same standard of living?

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Chapter 5: Index Numbers

Exercise 5.1Exercise 5.2Exercise 5.3Miscellaneous Exercise 5
Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 5 - Index Numbers

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 5 (Index Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 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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