Class 11 Commerce Economics - Index Numbers

The index number by the method of aggregates for the year $2010$ , taking $2000$ as the base year, was found to be $116$ . If sum of the prices in the year $2000$ is Rs. $300$ , find the values of $x$ and $y$ in the data given below:
Commodity $A$ $B$ $C$ $D$ $E$ $F$
Price in the year $2000$ (rs.) $50$ $x$ $30$ $70$ $116$ $20$
Price in the year $2010$ (rs.)
$60$ $24$ $y$ $80$ $120$ $28$

First we tabulate the given data in the following form:

Commodities	Price in $2000$ (in Rs.) ${P}_{0}$	Price in $2010$ (in Rs.) ${P}_{1}$
$A$	$50$	$60$
$B$	$x$	$24$
$C$	$30$	$y$
$D$	$70$	$80$
$E$	$116$	$120$
$F$	$20$	$28$
	$\sum { { P }_{ 0 } } =286+x$	$\sum { { P }_{ 1 } } =312+y$

Given:

$\sum { { P }_{ 0 } } =300$

$\Rightarrow$

$286+x=300\Rightarrow$

$x=14$
Index number

$=116$

$\therefore$ Using

${P}_{01}=\cfrac{\sum { { P }_{ 1 } } }{\sum { { P }_{ 0 } } }\times 100$

$116\times \cfrac{312+y}{300}\times 100$

$y=36$

$\therefore$

$x=14$ and

$y=36$

The price relatives and weight of a set commodities are given below:
Commodity A B C D
Price relative 125 120 127 119
Weight $x$ $2x$ $y$ $y+3$
If the sum of the weights is $40$ and weighted average of price relatives index number is $122$ , find the numerical values of $x$ and $y$ .

Commodity	Weight (w)	Price relative (p)	wp
A	$x$	$125$	$125x$
B	$2x$	$120$	$240x$
x	$y$	$127$	$127y$
D	$y+3$	$119$	$119y+357$
Sum	$3x+2y+3$		$356x+246y+357$

Sunm of weights

$=40$

$\Rightarrow 3x+2y+3=40$

$\Rightarrow 3x+2y=37$

Index number

$=122$

$\Rightarrow \dfrac{ 365x+246y+357 }{ 40 } =122\\ \Rightarrow 365x+246y=4523......(ii)$

Solving

$(i)$ and

$(ii)$

$\Rightarrow x=7,y=8$

Write any two uses of cost of living index number.

Uses of cost of living index number:
(i) It is used in wage negotiations, dearness allowance, bonus etc., to the workers.
(ii) The cost of living index number measures the change in the retail prices of a specified quantity of goods and services.
(iii) It is also useful to the government in framing policies relating to wages.
(iv) It is used as measures of change in the purchasing power of money and real income.

Calculate the cost of living index number of the following data-
Item Quantity
(in kg) Cost (in Rs.)
per kg in base year Cost (in Rs.)
per kg in current year
Sugar $5$ $17$ $16$
Tea $1$ $120$ $134$
Pulse $5$ $34$ $40$
Ghee $2$ $180$ $190$
Wheat $30$ $12$ $15$
Rice $8$ $20$ $22$

Items	Qty kg	Price in Rs./kg in base year	Price in Rs./kg in current year	Total cost of items (in Rs.) in base year	Total cost of items (in Rs.) in current year
Sugar	$5$	$17$	$16$	$85$	$80$
Tea	$1$	$120$	$134$	$120$	$134$
Pulses	$5$	$34$	$40$	$170$	$200$
Ghee	$2$	$180$	$190$	$360$	$380$
Wheat	$30$	$12$	$15$	$360$	$450$
Rice	$8$	$20$	$22$	$160$	$176$
Total				$1,255$	$1,420$

Cost of living index

$= \dfrac {\text {Total expenditure in current year}}{\text {Total expenditure in base year}}\times 100$

$= \dfrac {1420}{1255}\times 100$

$= \dfrac {142000}{1255} = 113.15$

Thus the cost living index

$= 113.15$ .

Match the following.
II Group-A Group-B
(1) USA (a) was established in 1990
(2) HDI (b) is in the medium HD group
(3) India (c) was established in 1979
(4) PQLI (d) is in the high HD group

1-d, 2-a, 3-b, 4-c.

Explain any three characteristics of index number.

Features of Index numbers are:

Average: They predict or represent the changes that take place in terms of averages.
Quantitative: They offer the accurate measurement of quantitative change.
Measures of relative changes: they measure relative changes over time.

Write the names of construction of index number.

Types of Methods of Construction:

Simple Method: Aggregative and Relative,
Weighted Method Aggregative and Relative.

Calculate age specific death (A-SDR) rates for the following data:
Age group (in years) Population
$('000)$ Number of Deaths
Below $10$ $25$ $50$
$10-30$ $30$ $90$
$30-45$ $40$ $160$
$45-70$ $20$ $100$

Age	No. of persons $/1000 \left( { { N }^{ P }x }/{ 100 } \right)$	No. of deaths $\left( { { N }^{ D }x } \right)$	$SDR=\left( \cfrac { { { N }^{ D }x } }{ { { N }^{ P }x } } \times 1000 \right)$
$<10$	$25$	$50$	$=2$
$10-30$	$30$	$90$	$3$
$30-45$	$40$	$160$	$4$
$45-70$	$20$	$100$	$5$

Calculate the cost of living index from the following data-
Items Annual Quantity Consumed
Base year Given year
Rice 2.5 Kg per month Rs. 12 per kg Rs. 25 per kg
Pulses 3 Kg per month Rs. 20 per kg Rs. 30 per kg
Oil 2 liter per month Rs. 25 per liter Rs. 35 per liter
Clothing 6 meters per month Rs. 5 per meter Rs. 7 per meter
Housing 12 month Rs. 40 per month Rs. 60 per month
Miscellaneous 12 month Rs. 15 per month Rs. 20 per month

2140835_2022178_ans_1844a8c5e931430688f7922e161b8266.png

Calculate Laspeyres index number, Paasches Index number, and Fishers ideal index number.
2015 2020
Price Quantity Price Quantity
100 1000 120 800
1500 180 2000 100
150 500 100 800
750 300 700 200
1200 120 1000 150

2143332_2023474_ans_8d70769e30214deab8b75f080608a6de.jpeg

"Index number is an economical barometers." Explain.

An index number is a number that expresses the relative change in magnitude of a variable or number of variables during a specified period. The variable may be the price of a certain commodity, the quantitative production of certain goods, or the cost of living.
It is a statistical device to measure the level of certain phenomena in comparison with a certain period known as the base period, which may be a week month, year, or group of years.
The index numbers are known as economic barometers or economic indicators since they help in understanding the changes in economic conditions of the society.

From the following data construct a price index no. by using - Laspeyre's method and Paasche's
method:
Commodity P0 Q0 P1 Q1
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 15

Solution is as follows:
2146911_2026094_ans_4b2e0b2e619a4bee83d6c296052b74be.PNG

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items P0 Q0 P1 Q1
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

Solution is as follows:
2148912_2027005_ans_1c7cd12306e4483c962b39148cca8344.PNG

With the help of the following data calculate the index number for 2010 taking 2009 as the base year with the help of the Simple aggregative method.
Commodity Price in 2009 Price in 2010
A 100 140
B 115 155
C 145 215
D 170 260
E 70 130

2139817_2022163_ans_0ed278d4c95944a4af5b891c07a3a85b.png

Calculate Laspeyer's & Paasche's Index number from the following data:
Items Price in 2011 Quantity in 2011 Price in 2019 Quantity in 2019
A 10 10 20 25
B 35 3 40 10
C 30 5 20 15
D 10 20 8 20
E 40 2 40 5

Solution is as follows:
2146909_2026092_ans_29d780e027bb432dbd4a62708be1efb0.PNG

Construct index of Industrial production of 2012 with the help of the below given data:
Industries Output
(units)
2002 2012 Weights
IT 75 300 25
Auto mobile 220 260 20
Mining 150 170 15
Rubber 90 45 10
Consumer producers 250 500 35
Iron and steel 300 450 30

2157148_2031166_ans_2c7d1df8b67e4138af0cc0e07d4b59f1.png

Calculate the Laspeyre's index number from the following information:

Commodities

Price in 2018 (P₀)

Quantity in 2018 (Q₀)

Price in 2020 (P₁)

A

3

1,000

5

B

2

1,500

4

C

2

1,200

3

D

5

1,800

6

Calculate index number by Laspeyre's method:

Goods

2020

2021`

P0

Q0
P1

Q1

A

2

10

1

6

B

5

5

2

4

C

3

10

1

2

D

4

2

1

1

E

2

1

3

5

Construct the price index by Laspeyre's and Paasche's method from the following information:

Commodities

Price in 2000 ( Rs.)

Quantity in 2000

Price in 2020 (Rs.)

Quantity in 2020

A

10

30

12

50

B

8

15

10

25

C

6

20

6

30

D

4

10

6

20

Solution is given by:
2158204_2032317_ans_1adb6ee34d524b2ab7f58d77c4627949.PNG

From the following data, calculate price index numbers by: (i) Laspeyer's method and (ii) Paasche's method

Items

Price (P0)

Quantity (Q0)

Price (P1)

Quantity (Q1)

A

20

8

40

6

B

50

10

60

5

C

40

15

50

15

D

20

20

20

25

Calculate index number of the following table, using Paasche's method:
Commodities
Base Year
Current Year
P0
Q0
P1
Q1
A
2
10
4
5
B
5
12
6
10
C
4
20
5
15
D
2
15
3
10

Calculate index number of the following table, using Laspeyre's method:

Commodities

Base Year

Current Year

P0

Q0
P1

Q1

A

2

10

4

5

B

5

12

6

10

C

4

20

5

15

D

2

15

3

10

Calculate index number by Paasche's method:
Goods
2020
2021`
P0
Q0
P1
Q1
A
2
10
1
6
B
5
5
2
4
C
3
10
1
2
D
4
2
1
1
E
2
1
3
5

The price of six different commodities for year $2009$ and year $2011$ are as follows:
Commodities $A$ $B$ $C$ $D$ $E$ $F$
Price in $2009 (Rs)$ $35$ $80$ $25$ $30$ $80$ $x$
Price in $2011 (Rs)$ $50$ $y$ $45$ $70$ $120$ $105$
The Index number for the year $2011$ taking $2009$ as the base year for the above data was calculated to be $124$ . Find the values of $x$ and $y$ if the total price in $2009$ is $Rs. 360$

Commodities	Prices in $2009$	Prices in $2011$
$A$	$35$	$50$
$B$	$80$	$y$
$C$	$25$	$45$
$D$	$30$	$70$
$E$	$80$	$120$
$F$	$x$	$105$
	$\sum P_{0} = 250 + x$	$\sum P_{1} = 390 + y$

Given,

$\sum P_{0} = 360$

$x + 250 = 360$

$x = 110$

$\dfrac {\sum P_{1}}{\sum P_{0}} \times 100 = P_{01}$

$\dfrac {390 + y}{360} \times 100 = 125$

$390 + y = \dfrac {125\times 360}{100}$

$390 + y = 450$

$y = 60$

Hence, the value of

$x$ is

$Rs. 110$ and

$y$ is

$Rs. 60$ .

Calculate the index number for the year $2014$ , with $2010$ as the base year by the weighted aggregate method from the following data :
Commodity Price in rupees $(2010)$ Price in rupees $(2014)$ Weight
$A$ $2$ $4$ $8$
$B$ $5$ $6$ $10$
$C$ $4$ $5$ $14$
$D$ $2$ $2$ $19$

Commodity	Price in Year $2010$ ( $p_0$ )	Price in Year $2014$ ( $p_1$ )	Weight $w$	$p_0w$	$p_1w$
$A$	$02$	$04$	$08$	$16$	$32$
$B$	$05$	$06$	$10$	$50$	$60$
$C$	$04$	$05$	$14$	$56$	$70$
$D$	$02$	$02$	$19$	$38$	$38$
Total				$\sum p_0w = 160$	$\sum p_1w = 200$

Using weighted aggregate method, the required price index

$=\dfrac{\sum p_1w}{\sum p_0w}\times 100=\dfrac{200}{160}\times 100 = 125$ .

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items Price of base year (Rs.) Quantity of base year Price of current year Quantity of current year
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

Solution is as follows:
2150271_2027701_ans_0df077c198134afba23f603d38b561a0.PNG

Calculate Laspeyre's Index number and Paasche's Index number.

2019

2020

Commodity
Price (P0)

Quantity (Q0)
Price (P1)

Price (Q1)

A

100

200

110

150

B

25

400

30

200

C

1,100

10

900

15

D

50

500

40

60

E

10

1,000

12

900

Solution is given by:
2157600_2031928_ans_b2e4c0fc6ebe4b278207a30b2e301f07.PNG

Calculate cost of living index, for the following data, using aggregate expenditure and family budget Method.
Commodity Price in 2011 Price in 2016 Quantity in 2011
A 10 15 15
B 8 12 20
C 20 24 10
D 32 40 5
E 15 20 6
F 12 18 2
G 8 10 1

Solution is given as:
2150266_2027696_ans_46d9d165f77c4f8aa2d9f61a46ff2b89.jpeg

From the following data, calculate price index numbers for 2016 with 2011 as base by:
Laspeyre's Method,
Paasche's Method,
Fisher's Method.
Commodity Price 2011 Quantity 2011 Price 2016 Quantity 2016
A 20 8 40 6
B 50 10 60 5
C 40 15 50 15
D 20 20 20 25

Solution is give as follows:
2150267_2027697_ans_99a44fa583204a749c8cf3113472a52a.PNG

Construct quantity index number of 2019 from the following data by:
(a) Laspeyre's method, and (b) Paasche's ethod

2018

2019

Commodity
Price

Quantity
Price

Quantity

A

20

60

24

100

B

16

30

20

50

C

12

40

12

60

D

8

20

12

40

Solution is given by:
2157601_2031929_ans_d110ddb9b4044fe190c3aa5efb5a269f.PNG

Index Numbers - Class 11 Commerce Economics - Extra Questions

The price relatives and weight of a set commodities are given below:
Commodity A B C D
Price relative 125 120 127 119
Weight $x$ $2x$ $y$ $y+3$
If the sum of the weights is $40$ and weighted average of price relatives index number is $122$ , find the numerical values of $x$ and $y$ .

Write any two uses of cost of living index number.

Calculate the cost of living index number of the following data-
Item Quantity
(in kg) Cost (in Rs.)
per kg in base year Cost (in Rs.)
per kg in current year
Sugar $5$ $17$ $16$
Tea $1$ $120$ $134$
Pulse $5$ $34$ $40$
Ghee $2$ $180$ $190$
Wheat $30$ $12$ $15$
Rice $8$ $20$ $22$

Match the following.
II Group-A Group-B
(1) USA (a) was established in 1990
(2) HDI (b) is in the medium HD group
(3) India (c) was established in 1979
(4) PQLI (d) is in the high HD group

Explain any three characteristics of index number.

Write the names of construction of index number.

Calculate age specific death (A-SDR) rates for the following data:
Age group (in years) Population
$('000)$ Number of Deaths
Below $10$ $25$ $50$
$10-30$ $30$ $90$
$30-45$ $40$ $160$
$45-70$ $20$ $100$

Calculate Laspeyres index number, Paasches Index number, and Fishers ideal index number.
2015 2020
Price Quantity Price Quantity
100 1000 120 800
1500 180 2000 100
150 500 100 800
750 300 700 200
1200 120 1000 150

"Index number is an economical barometers." Explain.

From the following data construct a price index no. by using - Laspeyre's method and Paasche's
method:
Commodity P0 Q0 P1 Q1
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 15

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items P0 Q0 P1 Q1
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

With the help of the following data calculate the index number for 2010 taking 2009 as the base year with the help of the Simple aggregative method.
Commodity Price in 2009 Price in 2010
A 100 140
B 115 155
C 145 215
D 170 260
E 70 130

Calculate Laspeyer's & Paasche's Index number from the following data:
Items Price in 2011 Quantity in 2011 Price in 2019 Quantity in 2019
A 10 10 20 25
B 35 3 40 10
C 30 5 20 15
D 10 20 8 20
E 40 2 40 5

Construct index of Industrial production of 2012 with the help of the below given data:
Industries Output
(units)
2002 2012 Weights
IT 75 300 25
Auto mobile 220 260 20
Mining 150 170 15
Rubber 90 45 10
Consumer producers 250 500 35
Iron and steel 300 450 30

Calculate the Laspeyre's index number from the following information:

Commodities

Price in 2018 (P₀)

Quantity in 2018 (Q₀)

Price in 2020 (P₁)

A

3

1,000

5

B

2

1,500

4

C

2

1,200

3

D

5

1,800

6

Calculate index number by Laspeyre's method:

Goods

2020

2021`

P0

Q0
P1

Q1

A

2

10

1

6

B

5

5

2

4

C

3

10

1

2

D

4

2

1

1

E

2

1

3

5

Construct the price index by Laspeyre's and Paasche's method from the following information:

Commodities

Price in 2000 ( Rs.)

Quantity in 2000

Price in 2020 (Rs.)

Quantity in 2020

A

10

30

12

50

B

8

15

10

25

C

6

20

6

30

D

4

10

6

20

From the following data, calculate price index numbers by: (i) Laspeyer's method and (ii) Paasche's method

Items

Price (P0)

Quantity (Q0)

Price (P1)

Quantity (Q1)

A

20

8

40

6

B

50

10

60

5

C

40

15

50

15

D

20

20

20

25

Calculate index number of the following table, using Paasche's method:
Commodities
Base Year
Current Year
P0
Q0
P1
Q1
A
2
10
4
5
B
5
12
6
10
C
4
20
5
15
D
2
15
3
10

Calculate index number of the following table, using Laspeyre's method:

Commodities

Base Year

Current Year

P0

Q0
P1

Q1

A

2

10

4

5

B

5

12

6

10

C

4

20

5

15

D

2

15

3

10

Calculate index number by Paasche's method:
Goods
2020
2021`
P0
Q0
P1
Q1
A
2
10
1
6
B
5
5
2
4
C
3
10
1
2
D
4
2
1
1
E
2
1
3
5

Calculate the index number for the year $2014$ , with $2010$ as the base year by the weighted aggregate method from the following data :
Commodity Price in rupees $(2010)$ Price in rupees $(2014)$ Weight
$A$ $2$ $4$ $8$
$B$ $5$ $6$ $10$
$C$ $4$ $5$ $14$
$D$ $2$ $2$ $19$

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items Price of base year (Rs.) Quantity of base year Price of current year Quantity of current year
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

Calculate Laspeyre's Index number and Paasche's Index number.

2019

2020

Commodity
Price (P0)

Quantity (Q0)
Price (P1)

Price (Q1)

A

100

200

110

150

B

25

400

30

200

C

1,100

10

900

15

D

50

500

40

60

E

10

1,000

12

900

Calculate cost of living index, for the following data, using aggregate expenditure and family budget Method.
Commodity Price in 2011 Price in 2016 Quantity in 2011
A 10 15 15
B 8 12 20
C 20 24 10
D 32 40 5
E 15 20 6
F 12 18 2
G 8 10 1

From the following data, calculate price index numbers for 2016 with 2011 as base by:
Laspeyre's Method,
Paasche's Method,
Fisher's Method.
Commodity Price 2011 Quantity 2011 Price 2016 Quantity 2016
A 20 8 40 6
B 50 10 60 5
C 40 15 50 15
D 20 20 20 25

Construct quantity index number of 2019 from the following data by:
(a) Laspeyre's method, and (b) Paasche's ethod

2018

2019

Commodity
Price

Quantity
Price

Quantity

A

20

60

24

100

B

16

30

20

50

C

12

40

12

60

D

8

20

12

40

Class 11 Commerce Economics Extra Questions

Commodity	$A$	$B$	$C$	$D$	$E$	$F$
Price in the year $2000$ (rs.)	$50$	$x$	$30$	$70$	$116$	$20$
Price in the year $2010$ (rs.)	$60$	$24$	$y$	$80$	$120$	$28$

Commodity	A	B	C	D
Price relative	125	120	127	119
Weight	$x$	$2x$	$y$	$y+3$

Item	Quantity (in kg)	Cost (in Rs.) per kg in base year	Cost (in Rs.) per kg in current year
Sugar	$5$	$17$	$16$
Tea	$1$	$120$	$134$
Pulse	$5$	$34$	$40$
Ghee	$2$	$180$	$190$
Wheat	$30$	$12$	$15$
Rice	$8$	$20$	$22$

II	Group-A		Group-B
(1)	USA	(a)	was established in 1990
(2)	HDI	(b)	is in the medium HD group
(3)	India	(c)	was established in 1979
(4)	PQLI	(d)	is in the high HD group

Age group (in years)	Population $('000)$	Number of Deaths
Below $10$	$25$	$50$
$10-30$	$30$	$90$
$30-45$	$40$	$160$
$45-70$	$20$	$100$

Items	Annual Quantity Consumed
		Base year	Given year
Rice	2.5 Kg per month	Rs. 12 per kg	Rs. 25 per kg
Pulses	3 Kg per month	Rs. 20 per kg	Rs. 30 per kg
Oil	2 liter per month	Rs. 25 per liter	Rs. 35 per liter
Clothing	6 meters per month	Rs. 5 per meter	Rs. 7 per meter
Housing	12 month	Rs. 40 per month	Rs. 60 per month
Miscellaneous	12 month	Rs. 15 per month	Rs. 20 per month

2015		2020
Price	Quantity	Price	Quantity
100	1000	120	800
1500	180	2000	100
150	500	100	800
750	300	700	200
1200	120	1000	150

Commodity	Price in 2009	Price in 2010
A	100	140
B	115	155
C	145	215
D	170	260
E	70	130

Items	Price in 2011	Quantity in 2011	Price in 2019	Quantity in 2019
A	10	10	20	25
B	35	3	40	10
C	30	5	20	15
D	10	20	8	20
E	40	2	40	5

Industries		Output (units)
	2002	2012	Weights
IT	75	300	25
Auto mobile	220	260	20
Mining	150	170	15
Rubber	90	45	10
Consumer producers	250	500	35
Iron and steel	300	450	30

Commodities	Price in 2018 (P₀)	Quantity in 2018 (Q₀)	Price in 2020 (P₁)
A	3	1,000	5
B	2	1,500	4
C	2	1,200	3
D	5	1,800	6

Commodities	Price in 2000 ( Rs.)	Quantity in 2000	Price in 2020 (Rs.)	Quantity in 2020
A	10	30	12	50
B	8	15	10	25
C	6	20	6	30
D	4	10	6	20

Items	Price (P0)	Quantity (Q0)	Price (P1)	Quantity (Q1)
A	20	8	40	6
B	50	10	60	5
C	40	15	50	15
D	20	20	20	25

Commodities	Base Year		Current Year
Commodities	P0	Q0	P1	Q1
A	2	10	4	5
B	5	12	6	10
C	4	20	5	15
D	2	15	3	10

Commodities	$A$	$B$	$C$	$D$	$E$	$F$
Price in $2009 (Rs)$	$35$	$80$	$25$	$30$	$80$	$x$
Price in $2011 (Rs)$	$50$	$y$	$45$	$70$	$120$	$105$

Commodity	Price in rupees $(2010)$	Price in rupees $(2014)$	Weight
$A$	$2$	$4$	$8$
$B$	$5$	$6$	$10$
$C$	$4$	$5$	$14$
$D$	$2$	$2$	$19$

Items	Price of base year (Rs.)	Quantity of base year	Price of current year	Quantity of current year
A	10	4	12	6
B	15	6	20	4
C	2	5	5	3
D	4	4	4	4

	2019		2020
Commodity	Price (P0)	Quantity (Q0)	Price (P1)	Price (Q1)
A	100	200	110	150
B	25	400	30	200
C	1,100	10	900	15
D	50	500	40	60
E	10	1,000	12	900

Commodity	Price in 2011	Price in 2016	Quantity in 2011
A	10	15	15
B	8	12	20
C	20	24	10
D	32	40	5
E	15	20	6
F	12	18	2
G	8	10	1

Commodity	Price 2011	Quantity 2011	Price 2016	Quantity 2016
A	20	8	40	6
B	50	10	60	5
C	40	15	50	15
D	20	20	20	25

Index Numbers - Class 11 Commerce Economics - Extra Questions

The price relatives and weight of a set commodities are given below:CommodityABCDPrice relative125120127119Weightxx2x2xyyy+3y+3If the sum of the weights is 4040 and weighted average of price relatives index number is 122122, find the numerical values of xx and yy.

Write any two uses of cost of living index number.

Calculate the cost of living index number of the following data-ItemQuantity(in kg)Cost (in Rs.)per kg in base yearCost (in Rs.)per kg in current yearSugar5517171616Tea11120120134134Pulse5534344040Ghee22180180190190Wheat303012121515Rice8820202222

Match the following.IIGroup-AGroup-B(1)USA(a)was established in 1990(2)HDI(b) is in the medium HD group(3)India(c)was established in 1979(4)PQLI(d)is in the high HD group

Explain any three characteristics of index number.

Write the names of construction of index number.

Calculate age specific death (A-SDR) rates for the following data:Age group (in years)Population('000)('000)Number of DeathsBelow 10102525505010-3010-303030909030-4530-45404016016045-7045-702020100100

Calculate Laspeyres index number, Paasches Index number, and Fishers ideal index number.20152020Price QuantityPriceQuantity10010001208001500180200010015050010080075030070020012001201000150

"Index number is an economical barometers." Explain.

From the following data construct a price index no. by using - Laspeyre's method and Paasche'smethod:CommodityP0Q0P1Q1A2846B51065C414510D219215

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table: ItemsP0 Q0 P1 Q1 A 10 4 12 6 B 15 6 20 4 C 2 5 5 3 D 4 4 4 4

With the help of the following data calculate the index number for 2010 taking 2009 as the base year with the help of the Simple aggregative method.CommodityPrice in 2009Price in 2010A100140B115155C145215D170260E70130

Calculate Laspeyer's & Paasche's Index number from the following data:ItemsPrice in 2011Quantity in 2011Price in 2019Quantity in 2019A10102025B3534010C3052015D1020820E402405

Construct index of Industrial production of 2012 with the help of the below given data:IndustriesOutput(units)20022012WeightsIT7530025Auto mobile22026020Mining15017015Rubber904510Consumer producers25050035Iron and steel 30045030

Calculate the Laspeyre's index number from the following information: Commodities Price in 2018 (P0) Quantity in 2018 (Q0) Price in 2020 (P1) A 3 1,000 5 B 2 1,500 4 C 2 1,200 3 D 5 1,800 6

Calculate index number by Laspeyre's method: Goods 2020 2021` P0 Q0 P1 Q1 A 2 10 1 6 B 5 5 2 4 C 3 10 1 2 D 4 2 1 1 E 2 1 3 5

Construct the price index by Laspeyre's and Paasche's method from the following information: Commodities Price in 2000 ( Rs.) Quantity in 2000 Price in 2020 (Rs.) Quantity in 2020 A 10 30 12 50 B 8 15 10 25 C 6 20 6 30 D 4 10 6 20

From the following data, calculate price index numbers by: (i) Laspeyer's method and (ii) Paasche's method Items Price (P0) Quantity (Q0) Price (P1) Quantity (Q1) A 20 8 40 6 B 50 10 60 5 C 40 15 50 15 D 20 20 20 25

Calculate index number of the following table, using Paasche's method:CommoditiesBase YearCurrent YearP0Q0P1Q1A21045B512610C420515D215310

Calculate index number of the following table, using Laspeyre's method: Commodities Base Year Current Year P0 Q0 P1 Q1 A 2 10 4 5 B 5 12 6 10 C 4 20 5 15 D 2 15 3 10

Calculate index number by Paasche's method:Goods20202021`P0Q0 P1Q1A21016B5524C31012D4211E2135

Calculate the index number for the year 20142014, with 20102010 as the base year by the weighted aggregate method from the following data :Commodity Price in rupees (2010)(2010)Price in rupees (2014)(2014) WeightAA224488BB55661010CC44551414DD22221919

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:ItemsPrice of base year (Rs.)Quantity of base yearPrice of current yearQuantity of current yearA104126B156204C2553D4444

Calculate Laspeyre's Index number and Paasche's Index number. 2019 2020 Commodity Price (P0) Quantity (Q0) Price (P1) Price (Q1) A 100 200 110 150 B 25 400 30 200 C 1,100 10 900 15 D 50 500 40 60 E 10 1,000 12 900

Calculate cost of living index, for the following data, using aggregate expenditure and family budget Method.CommodityPrice in 2011Price in 2016Quantity in 2011A101515B81220C202410D32405E15206F12182G8101

From the following data, calculate price index numbers for 2016 with 2011 as base by:Laspeyre's Method,Paasche's Method,Fisher's Method.CommodityPrice 2011Quantity 2011Price 2016Quantity 2016A208406B5010605C40155015D20202025

Construct quantity index number of 2019 from the following data by:(a) Laspeyre's method, and (b) Paasche's ethod 2018 2019 Commodity Price Quantity Price Quantity A 20 60 24 100 B 16 30 20 50 C 12 40 12 60 D 8 20 12 40

Class 11 Commerce Economics Extra Questions

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The price relatives and weight of a set commodities are given below:
Commodity A B C D
Price relative 125 120 127 119
Weight $x$ $2x$ $y$ $y+3$
If the sum of the weights is $40$ and weighted average of price relatives index number is $122$ , find the numerical values of $x$ and $y$ .

Calculate the cost of living index number of the following data-
Item Quantity
(in kg) Cost (in Rs.)
per kg in base year Cost (in Rs.)
per kg in current year
Sugar $5$ $17$ $16$
Tea $1$ $120$ $134$
Pulse $5$ $34$ $40$
Ghee $2$ $180$ $190$
Wheat $30$ $12$ $15$
Rice $8$ $20$ $22$

Match the following.
II Group-A Group-B
(1) USA (a) was established in 1990
(2) HDI (b) is in the medium HD group
(3) India (c) was established in 1979
(4) PQLI (d) is in the high HD group

Calculate age specific death (A-SDR) rates for the following data:
Age group (in years) Population
$('000)$ Number of Deaths
Below $10$ $25$ $50$
$10-30$ $30$ $90$
$30-45$ $40$ $160$
$45-70$ $20$ $100$

Calculate Laspeyres index number, Paasches Index number, and Fishers ideal index number.
2015 2020
Price Quantity Price Quantity
100 1000 120 800
1500 180 2000 100
150 500 100 800
750 300 700 200
1200 120 1000 150

From the following data construct a price index no. by using - Laspeyre's method and Paasche's
method:
Commodity P0 Q0 P1 Q1
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 15

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items P0 Q0 P1 Q1
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

With the help of the following data calculate the index number for 2010 taking 2009 as the base year with the help of the Simple aggregative method.
Commodity Price in 2009 Price in 2010
A 100 140
B 115 155
C 145 215
D 170 260
E 70 130

Calculate Laspeyer's & Paasche's Index number from the following data:
Items Price in 2011 Quantity in 2011 Price in 2019 Quantity in 2019
A 10 10 20 25
B 35 3 40 10
C 30 5 20 15
D 10 20 8 20
E 40 2 40 5

Construct index of Industrial production of 2012 with the help of the below given data:
Industries Output
(units)
2002 2012 Weights
IT 75 300 25
Auto mobile 220 260 20
Mining 150 170 15
Rubber 90 45 10
Consumer producers 250 500 35
Iron and steel 300 450 30

Calculate the Laspeyre's index number from the following information:

Commodities

Price in 2018 (P₀)

Quantity in 2018 (Q₀)

Price in 2020 (P₁)

A

3

1,000

5

B

2

1,500

4

C

2

1,200

3

D

5

1,800

6

Calculate index number by Laspeyre's method:

Goods

2020

2021`

P0

Q0
P1

Q1

A

2

10

1

6

B

5

5

2

4

C

3

10

1

2

D

4

2

1

1

E

2

1

3

5

Construct the price index by Laspeyre's and Paasche's method from the following information:

Commodities

Price in 2000 ( Rs.)

Quantity in 2000

Price in 2020 (Rs.)

Quantity in 2020

A

10

30

12

50

B

8

15

10

25

C

6

20

6

30

D

4

10

6

20

From the following data, calculate price index numbers by: (i) Laspeyer's method and (ii) Paasche's method

Items

Price (P0)

Quantity (Q0)

Price (P1)

Quantity (Q1)

A

20

8

40

6

B

50

10

60

5

C

40

15

50

15

D

20

20

20

25

Calculate index number of the following table, using Paasche's method:
Commodities
Base Year
Current Year
P0
Q0
P1
Q1
A
2
10
4
5
B
5
12
6
10
C
4
20
5
15
D
2
15
3
10

Calculate index number of the following table, using Laspeyre's method:

Commodities

Base Year

Current Year

P0

Q0
P1

Q1

A

2

10

4

5

B

5

12

6

10

C

4

20

5

15

D

2

15

3

10

Calculate index number by Paasche's method:
Goods
2020
2021`
P0
Q0
P1
Q1
A
2
10
1
6
B
5
5
2
4
C
3
10
1
2
D
4
2
1
1
E
2
1
3
5

Calculate the index number for the year $2014$ , with $2010$ as the base year by the weighted aggregate method from the following data :
Commodity Price in rupees $(2010)$ Price in rupees $(2014)$ Weight
$A$ $2$ $4$ $8$
$B$ $5$ $6$ $10$
$C$ $4$ $5$ $14$
$D$ $2$ $2$ $19$

Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
Items Price of base year (Rs.) Quantity of base year Price of current year Quantity of current year
A 10 4 12 6
B 15 6 20 4
C 2 5 5 3
D 4 4 4 4

Calculate Laspeyre's Index number and Paasche's Index number.

2019

2020

Commodity
Price (P0)

Quantity (Q0)
Price (P1)

Price (Q1)

A

100

200

110

150

B

25

400

30

200

C

1,100

10

900

15

D

50

500

40

60

E

10

1,000

12

900

Calculate cost of living index, for the following data, using aggregate expenditure and family budget Method.
Commodity Price in 2011 Price in 2016 Quantity in 2011
A 10 15 15
B 8 12 20
C 20 24 10
D 32 40 5
E 15 20 6
F 12 18 2
G 8 10 1

From the following data, calculate price index numbers for 2016 with 2011 as base by:
Laspeyre's Method,
Paasche's Method,
Fisher's Method.
Commodity Price 2011 Quantity 2011 Price 2016 Quantity 2016
A 20 8 40 6
B 50 10 60 5
C 40 15 50 15
D 20 20 20 25

Construct quantity index number of 2019 from the following data by:
(a) Laspeyre's method, and (b) Paasche's ethod

2018

2019

Commodity
Price

Quantity
Price

Quantity

A

20

60

24

100

B

16

30

20

50

C

12

40

12

60

D

8

20

12

40

	2018		2019
Commodity	Price	Quantity	Price	Quantity
A	20	60	24	100
B	16	30	20	50
C	12	40	12	60
D	8	20	12	40