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Index Numbers - Class 11 Commerce Economics - Extra Questions

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:
CommodityABCDEF
Price in the year 2000(rs.)50x307011620
Price in the year 2010(rs.)
6024y8012028



The price relatives and weight of a set commodities are given below:
CommodityABCD
Price relative125120127119
Weightx2xyy+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-
ItemQuantity
(in kg)
Cost (in Rs.)
per kg in base year
Cost (in Rs.)
per kg in current year
Sugar51716
Tea1120134
Pulse53440
Ghee2180190
Wheat301215
Rice82022



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)
Number of Deaths
Below 102550
10303090
304540160
457020100



Calculate the cost of living index from the following data-
ItemsAnnual Quantity Consumed
Base yearGiven year
Rice2.5 Kg per monthRs. 12 per kgRs. 25 per kg
Pulses3 Kg per monthRs. 20 per kgRs. 30 per kg
Oil2 liter per monthRs. 25 per literRs. 35 per liter
Clothing6 meters per monthRs. 5 per meterRs. 7 per meter
Housing12 monthRs. 40 per monthRs. 60 per month
Miscellaneous12 monthRs. 15 per monthRs. 20 per month



Calculate Laspeyres index number, Paasches Index number, and Fishers ideal index number.
20152020
Price QuantityPriceQuantity
1001000120800
15001802000100
150500100800
750300700200
12001201000150



"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:
CommodityP0Q0P1Q1
A2846
B51065
C414510
D219215



Compute (i) Laspeyre's (ii) Paashe's Index number from the following table:
 ItemsP0 Q0 P1 Q1 
10 12 
15 20 



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 2010
A100140
B115155
C145215
D170260
E70130



Calculate Laspeyer's & Paasche's Index number from the following data:
ItemsPrice in 2011Quantity in 2011Price in 2019Quantity in 2019
A10102025
B3534010
C3052015
D1020820
E402405



Construct index of Industrial production of 2012 with the help of the below given data:
IndustriesOutput
(units)
20022012Weights
IT7530025
Auto mobile22026020
Mining15017015
Rubber904510
Consumer producers25050035
Iron 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:

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:
CommoditiesABCDEF
Price in 2009(Rs)3580253080x
Price in 2011(Rs)50y4570120105
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



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
A248
B5610
C4514
D2219



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 year
A104126
B156204
C2553
D4444



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 2011
A101515
B81220
C202410
D32405
E15206
F12182
G8101



From the following data, calculate price index numbers for 2016 with 2011 as base by:
  1. Laspeyre's Method,
  2. Paasche's Method,
  3. Fisher's Method.
    CommodityPrice 2011Quantity 2011Price 2016Quantity 2016
    A208406
    B5010605
    C40155015
    D20202025



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