TR Jain & Vk Ohri (2016) Solutions for Class 11 Humanities Economics Chapter 13 Index Numbers are provided here with simple step-by-step explanations. These solutions for Index Numbers are extremely popular among class 11 Humanities students for Economics Index Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the TR Jain & Vk Ohri (2016) Book of class 11 Humanities Economics Chapter 13 are provided here for you for free. You will also love the ad-free experience on Meritnation’s TR Jain & Vk Ohri (2016) Solutions. All TR Jain & Vk Ohri (2016) Solutions for class 11 Humanities Economics are prepared by experts and are 100% accurate.
Page No 351:
Question 1:
Using Simple Aggregate Method and Price Relatives Method, find out index values for the year 2017 from the following data:
Itmes | A | B | C | D | E |
2004 Price (â¹) | 15 | 33 | 38 | 25 | 50 |
2017 Price (â¹) | 30 | 35 | 57 | 35 | 63 |
Answer:
Simple Aggregate Method
Items | 2004 Price (P0) |
2014 Price (P1) |
A B C D E |
15 33 38 25 50 |
30 35 57 35 63 |
ΣP0 = 161 | ΣP1 = 220 |
Price Relative Method
Items | 2004 Price
(P0)
|
2014 Price (P1) |
Price relative =
|
A | 15 | 30 | |
B | 33 | 35 | |
C | 38 | 57 | |
D | 25 | 35 | |
E | 50 | 63 | |
N = 5 |
Page No 351:
Question 2:
Find out index value by the Price Relative Method for the year 2017 from the following data:
Items | A | B | C | D | E | F | G |
2004 Price (â¹) | 100 | 10 | 5 | 4 | 1 | 2 | 3 |
2017 Price (â¹) | 100 | 9 | 4 | 2 | 1 | 2.50 | 2.25 |
Answer:
Items |
2004 Price
(P0)
|
2014 Price |
Price relative |
A | 100 | 100 | |
B | 10 | 9 | |
C | 5 | 4 | |
D | 4 | 2 | |
E | 1 | 1 | |
F | 2 | 2.50 | |
G | 3 | 2.25 | |
N = 7 |
Hence, Price Index = 88.57
Page No 351:
Question 3:
Construct an index number by Price Relatives Method using 2004 as base year:
Goods | A | B | C | D |
2004 Price (â¹) | 8 | 10 | 15 | 20 |
2016 Price (â¹) | 10 | 12 | 18 | 22 |
2017 Price (â¹) | 12 | 14 | 20 | 25 |
Answer:
Goods | 2004 Price (P0) |
2013 Price (P1) |
2014 Price (P2) |
Price relatives of 2013 in relation to 2004 |
Price relatives of 2014 in relation to 2004 |
A | 8 | 10 | 12 | ||
B | 10 | 12 | 14 | ||
C | 15 | 18 | 20 | ||
D | 20 | 22 | 25 | ||
N=4 |
Page No 351:
Question 4:
Construct and index of prices using 2004 as the base year and Price Relatives Method:
Goods | Weight | 2014 | 2016 | 2017 |
A B C |
5 3 2 |
10 5 4 |
12 6 5 |
14 8 7 |
Answer:
Construction of Price Index for the year 2013
Goods | Weight (W) |
2004 Price (P0) |
2013 Price (P1) |
RW | |
A | 5 | 10 | 12 | 600 | |
B | 3 | 5 | 6 | 360 | |
C | 2 | 4 | 5 | 250 | |
ΣW = 10 | ΣRW = 1210 |
Construction of Price Index for the year 2014
Goods | Weight (W) |
2004 Price (P0) |
2014 Price (P2) |
RW | |
A | 5 | 10 | 14 | 700 | |
B | 3 | 5 | 8 | 480 | |
C | 2 | 4 | 7 | 350 | |
ΣW = 10 | ΣRW = 1530 |
Page No 370:
Question 1:
Taking 2004 as base year, construct the index numbers of the years 2005 and 2009.
Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 |
Prices (â¹) | 10 | 14 | 16 | 20 | 22 | 24 |
Answer:
Year | Price |
2004 | 10 |
2005 | |
2006 | 16 |
2007 | 20 |
2008 | 22 |
2009 |
Since, base year is given as 2004
∴ P0 = 10
Index number for year 2005
Here, P1 = 14
Index number for year 2009
Here, P1 = 24
Substituting the values in the formula
Page No 370:
Question 2:
Construct index number by Price Relative Method taking 2004 as base year:
Price per Unit in â¹ |
Year | A | B | C | D |
2014 2015 2016 2017 |
25 20 25 28 |
18 22 20 24 |
16 24 25 30 |
21 22 25 26 |
Answer:
Here, we construct the index number for each of the years from 2012-2014.
Base Year 2004, Current year 2015
2004 ( P0) |
2015 (P1) |
Price Relative = | |
A | 25 | 20 | |
B | 18 | 22 | |
C | 16 | 24 | |
D | 21 | 22 | |
∑ =456.96 |
According to the Price Relative Method, price index is calculated using the following formula.
Base Year 2004, Current year 2016
2004 (P0) |
2016 (P1) |
Price Relative = | |
A | 25 | 25 | |
B | 18 | 20 | |
C | 16 | 25 | |
D | 21 | 25 | |
∑= 486.4 |
Base Year 2004, Current Year 2017
2004 (P0) |
2017 (P1) |
Price Relative = | |
A | 25 | 28 | |
B | 18 | 24 | |
C | 16 | 30 | |
D | 21 | 26 | |
∑ 556.63 |
Page No 370:
Question 3:
Compute a Price Index for the following by (i) Simple Aggregative Method, and (ii) Average of Price Relative Method:
Commodities | A | B | C | D | E | F |
Price in 2009 (â¹) | 20 | 30 | 10 | 25 | 40 | 50 |
Price in 2017 (â¹) | 25 | 30 | 15 | 35 | 45 | 55 |
Answer:
(i) Simple Aggregate Method
2009 (P0) |
2017 (P1) |
|
A B C D E F |
20 30 10 25 40 50 |
25 30 15 35 45 55 |
∑P0 =â 175 | ∑P1 = 205 |
(ii) Price Relative Method
2009 â(P0) |
2017 â(P1) |
Price Relative = | |
A | 20 | 25 | |
B | 30 | 30 | |
C | 10 | 15 | |
D | 25 | 35 | |
E | 40 | 45 | |
F | 50 | 55 | |
∑ = 737.5 |
Page No 371:
Question 4:
Construct price index number of the following data by using:
(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.
Items | Base Year | Current Year | ||
Quantity | Price | Quantity | Price | |
A B C D |
3 7 4 6 |
5 4 7 6 |
2 5 3 5 |
8 6 10 7 |
Answer:
q0 | p0 | p0q0 | p1 | q1 | p1q1 | p1q0 | p0q1 | |
A B C D |
3 7 4 6 |
5 4 7 6 |
15 28 28 36 |
8 6 10 7 |
2 5 3 5 |
16 30 30 35 |
24 42 40 42 |
10 20 21 30 |
(i) Laspeyre's Price index:
(ii) Paasche's Price index:
(iii) Fisher's Price index:
Page No 371:
Question 5:
Construct an index number for the year 2017, taking 2004 as base year by any method you deem ideal:
Year | Good I | Good II | Good III | |||
Price | Quantity | Price | Quantity | Price | Quantity | |
2004 2017 |
5 4 |
10 12 |
8 7 |
6 7 |
6 5 |
3 4 |
Answer:
P0 | q0 | P1 | q1 | P0q0 | P1q1 | P0q1 | P1q0 | |
I II III |
5 8 6 |
10 6 3 |
4 7 5 |
12 7 4 |
50 48 18 |
48 49 20 |
60 56 24 |
40 42 15 |
Fisher's Method
Page No 371:
Question 6:
Given the following data and taking 2004 as the base year, construct index of prices using:
(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.
Year | Commodities | |||||||
A | B | C | D | |||||
Price | Quantity | Price | Quantity | Price | Quantity | Price | Quantity | |
2004 2017 |
24 30 |
8 10 |
9 10 |
3 4 |
16 20 |
5 8 |
10 9 |
3 4 |
Answer:
P0 | q0 | P0q0 | P1 | q1 | P1q1 | P1q0 | P0q1 | |
A B C D |
24 9 16 10 |
8 3 5 3 |
192 27 80 30 |
30 10 20 9 |
10 4 8 4 |
300 40 160 36 |
240 30 100 27 |
240 36 128 40 |
∑P0q0 = 329 | ∑P1q1 = 536 | ∑P1q0 =397 | ∑P0q1â = 444 |
Laspeyre's Price index
Paasche's Price index
Fisher's Price index
Page No 371:
Question 7:
Construct a weighted index number of the following data using price relative method:
Item | A | B | C | D | E |
Base Year (Quantity) | 24 | 14 | 8 | 4 | 8 |
Base Year (Price) | 2 | 4 | 6 | 10 | 5 |
Current Year (Price) | 3 | 5 | 9 | 12 | 5 |
Answer:
P0 | q0 | P1 | P0q0 â(W) |
RW | ||
A | 2 | 24 | 3 | 48 | 7200 | |
B | 4 | 14 | 5 | 56 | 7000 | |
C | 6 | 8 | 9 | 48 | 7200 | |
D | 10 | 4 | 12 | 40 | 4800 | |
E | 5 | 8 | 5 | 40 | 4000 | |
Weighted index number
Page No 371:
Question 8:
Find out the index number of the following data with Laspeyre's Method:
Year | 2016 | 2017 | ||
Price | Quantity | Price | Quantity | |
A B |
70 62 |
7 3 |
80 74 |
6 2 |
Answer:
P0 | q0 | P0q0 | P1 | q1 | P1q0 | |
A B |
70 62 |
7 3 |
490 186 |
80 74 |
6 2 |
560 222 |
∑ P0q0 =676 | ∑P1q0= 782 |
Laspeyre's Price index
Page No 372:
Question 9:
Construct Index number of the following data with Laspeyre's and Paasche's Methods:
Commodity | Base Year | Current Year | ||
Quantity | Price | Quantity | Price | |
A B C |
10 8 5 |
0.80 0.85 1.30 |
11 9 5.5 |
0.70 0.90 0.80 |
Answer:
P0 | q0 | P0q0 | P1 | q1 | P1q1 | P0q1 | P1q0 | |
A B C |
0.8 0.85 1.35 |
10 8 5 |
8 6.8 6.5 |
0.7 0.9 0.8 |
11 9 5.5 |
7.7 8.1 4.4 |
8.8 7.65 7.15 |
7 7.2 4 |
Laspeyre's Price Index
Passche's Price index
Page No 372:
Question 10:
Construct index numbers of the following data by Fisher's Method:
Commodity | Base Year | Current Year | ||
Price | Value | Price | Value | |
A
B C D E |
3 5 6 4 8 |
18 35 42 32 24 |
7 10 11 6 9 |
10 100 55 60 36 |
Answer:
P0 | Value (Base Year) |
P0q0 | P1 | Value (Current Year) |
P1q1 | P1q0 | P0q1 | |||
A B C D E |
3 5 6 4 8 |
18 35 42 32 24 |
6 7 7 8 3 |
18 35 42 32 24 |
7 10 11 6 9 |
14 100 55 60 36 |
2 10 5 10 4 |
14 100 55 60 36 |
42 70 77 48 27 |
6 50 30 40 32 |
151 |
Fisher's Price Index
Page No 372:
Question 11:
Construct Cost of Living Index on the basis of the following data:
Items | Price | Weight |
Wheat Rice Maida Pulses Oil |
241 150 200 170 125 |
10 4 2 2 2 |
Answer:
Items | Price (P) |
Weights (W) |
PW |
Wheat Rice Maida Pulses Oil |
241 150 200 170 125 |
10 4 2 2 2 |
2410 600 400 340 250 |
∑W=20 | ∑PW = 4000 |
Cost of living Index
Page No 372:
Question 12:
Construct Consumer Price Index Number with the help of the following data:
Consumer Items | Price | Weight |
Food Fuel Cloth House Rent Miscellaneous |
125 120 66.67 120 150 |
40 10 25 15 10 |
Answer:
Items | Price (P) |
Weights (W) |
PW |
Food Fuel Cloth House rent Miscellaneous |
125 120 66.67 120 150 |
40 10 25 15 10 |
5000 1200 16 66.75 1800 1500 |
Consumer price index
Page No 373:
Question 13:
From the following data find Consumer Price Index or Cost of Living Index:
Items | Quantity Consumed in Current Year | Price in Base year | Price in Current Year |
Rice Pulses Oil Clothing Housing Miscellaneous |
30 qt 36 kg 24 l 72 metres per month per month |
12 0.4 1.5 0.75 20 20 |
25 0.6 2.2 10 30 15 |
Answer:
Items | q1 | P0 | P1 | P1q1 | P0q1 |
Rice Pulses Oil Clothing Housing Miscellaneous |
30 36 24 72 1 1 |
12 0.4 1.5 0.75 20 20 |
25 0.6 2.2 10 30 15 |
750 21.6 52.8 720 30 15 |
360 14.4 36 54 20 20 |
âNote that here we are given the current year quantities for different items. So, the Consumer Price Index is calculated using the following formula.
Page No 373:
Question 14:
Construct Cost of Living Index Number for the year 2017 from the following statistics:
Commodity | 2004 Price | 2004 Quantity | 2017 Price |
A B C D E |
25 36 12 6 28 |
16.0 7.0 3.5 2.5 4.0 |
35 48 16 10 28 |
Answer:
P0 | q0 | P1 | P1q0 | P0q0 | |
A B C D E |
25 36 12 6 28 |
16 7 3.5 2.5 4 |
35 48 16 10 28 |
560 336 56 25 112 |
400 252 42 15 112 |
Page No 373:
Question 15:
Find the Consumer Price Index from the following data. Using
(i) Aggregative Expenditure Method, and
(ii) Family Budget Method.
Is there any difference between the two results?
Commodity | Quantity Consumed in the year 2004 | Unit | Price in 2004 (â¹) | Price in 2017 (â¹) |
Rice Wheat Bajra Arhar Desi Ghee Sugar |
6 8 1 2 20 1 |
Quintal Quintal Quintal Quintal kg Quintal |
100 80 70 120 12 160 |
120 90 70 115 15 170 |
Answer:
q0 | P0 | P1 | W = P0q0 | P1q0 | WR | ||
Rice | 6 | 100 | 120 | 600 | 720 | 72,000 | |
Wheat | 8 | 80 | 90 | 640 | 720 | 72,000 | |
Bajra | 1 | 70 | 70 | 70 | 70 | 70,000 | |
Arhar | 2 | 120 | 115 | 240 | 230 | 22,999.2 | |
Ghee | 20 | 12 | 15 | 240 | 300 | 30,000 | |
Sugar | 1 | 160 | 170 | 160 | 170 | 17,000 | |
283999.2 |
(i) Aggregate expenditure methodâ
()
(ii) Family Budged Method
Yes, there is a difference between the values calculated by the two methods.
Difference = 145.64 – 113.33 = 32.31
Page No 373:
Question 16:
Construct index number of industrial production in the year 2017 from the following data on the basis of 2005's production:
Industry | Units | 2005 | 2017 | Weight |
Electrical and Electronics Metallurgical Mechanical Mining Textiles Miscellaneous |
Mill. Nos. Th. Tonnes Th. Tonnes Th. Tonnes Mill. Mtrs. Th. Tonnes |
12 22 72 100 60 123 |
70 37 105 123 130 270 |
36 12 10 22 8 12 |
Answer:
Industry | q0 | q1 | Weight (W) |
WR | |
Electronics | 12 | 70 | 36 | 20999.88 | |
Metallurgical | 22 | 37 | 12 | 2018.16 | |
Mechanical | 72 | 105 | 10 | 1458.3 | |
Mining | 100 | 123 | 22 | 2706 | |
Textiles | 60 | 130 | 8 | 1733.36 | |
Misce. | 123 | 270 | 12 | 2634.12 | |
∑W = 100 | ∑ WR = 31549.82 |
Index number of Industrial Production
Page No 374:
Question 17:
Construct index number of industrial production from the following data:
Item | Units | Production or Output | Weight | |
Base year | Current Year | |||
Mechanical Sugar and Tea Textile Mining Transportation Electricity and Electronics |
Mill. Nos. Th. Tonnes Mill. Mtrs. Th. Tonnes Mill. Nos. Mill. Nos. |
237 62 572 165 335 87 |
400 150 820 200 727 323 |
5 10 35 15 20 15 |
Answer:
Item | Base year (q0) |
Current year (q1) |
Relatives values | Weight (W) |
WR |
Mechanical | 237 | 400 | 168.78 | 5 | 843.85 |
Sugar and Tea | 62 | 150 | 241.19 | 10 | 2419.35 |
Textile | 572 | 820 | 143.35 | 35 | 5017.48 |
Mining | 165 | 200 | 121.21 | 15 | 1818.15 |
Transportation | 335 | 727 | 217.01 | 20 | 4340.2 |
Electricity and electronics | 87 | 323 | 371.26 | 15 | 5568.9 |
∑W = 100 | ∑RW = 20008.3 |
Index number of Industrial Production
Page No 374:
Question 18:
Construct index number of industrial production from the following data:
Industry | Number of Items | Weight | |
Base Year | Current Year | ||
Mining and Quarrying Manufacturing Electricity and Electronics |
35 413 10 |
107 1225 27 |
10 85 5 |
Answer:
Industry | Base year (q0) |
Current year (q1) |
Relatives values R |
Weight (W) |
WR |
Mining and quarrying Manufacturing Electricity and electronics |
35 413 10 |
107 1225 27 |
305.71 296.61 270 |
10 85 5 |
3057.1 25211.85 1350 |
∑W = 100 | ∑RW = 29618.95 |
Index number
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