# Sandeep Garg Solutions Class 11 Economics Chapter 9 - Index Numbers

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Here are some questions with solutions on Index numbers.

## Sandeep Garg Solutions Class 11 – Chapter 9

Question 1

Arrange an index number for the year 2015 on the basis of 2010 using the simple aggregative method:

 Goods Unit Cost 2010 2015 Potato Kilo 100 500 Tomato Kilo 400 250 Onion Kilo 200 400 Oil litre 4 5 Fabric meter 2 3

 Goods 2010 Price (P0) 2015 Price (P1) Potato Tomato Onion Oil Fabric 100 400 200 4 2 500 250 400 5 3 Î£P0 = 702 Î£P1 = 928

P01 =

$$\begin{array}{l}\frac{\sum P_{1}}{\sum P_{0}}\, X\, 100\end{array}$$

P01 =

$$\begin{array}{l}\frac{928}{702}\, X\, 100\end{array}$$

P01 = 132

Question 2

Form an index number using 2010 price:

 Items P Q R S T U Prices (2011) 220 50 370 110 70 90 Prices (2016) 250 80 500 130 72 100

 Items Price in 2011 (P0) Price in 2016 (P1) P Q R S T U 220 50 370 110 70 90 250 80 500 130 72 100 Î£P0 = 910 Î£P1 = 1152

P01 =

$$\begin{array}{l}\frac{\sum P_{1}}{\sum P_{0}}\, X\, 100\end{array}$$

P01 =

$$\begin{array}{l}\frac{1152}{910}\, X\, 100\end{array}$$

P01 = 126.59

Question 3

Prepare an index number for 2014 on the basis of 2010 from the below data using aggregate expenditure method.

 Particulars Quantity (kg.) Prices 2010 2014 G 9 21 25 H 6 20 22 I 4 19 23 J 3 9 10 K 3 5 9

 Article 2010 Price (P0) 2014 Price (P1) Quantity (Q0) P0Q0 P1Q0 G H I J K 21 20 19 9 5 25 22 23 10 9 9 6 4 3 3 189 120 76 27 15 225 132 92 30 27 Î£P0Q0 = 427 Î£P1Q0 = 506

The consumer price index for the year 2014 is

$$\begin{array}{l}\frac{\sum P_{1}Q_{0}}{\sum P_{0}Q_{0}}\,\, \times 100\end{array}$$

=

$$\begin{array}{l}\frac{506}{427}\, X\, 100\end{array}$$

= 118.50

Question 4

Calculate the consumer index number by using the family budget method.

 Items Quantity Base Price Year Current Price Year Rent 45 200 225 Food 20 300 350 Clothing 8 150 175 Fuel 10 100 110 Misc. 17 200 250

 Items Base Price Year (P0) Current Price Year (P1) $$\begin{array}{l}I \,=\, \frac{P_{1}}{P_{0}} \, \times \, 100\end{array}$$ Quantity (Q0) P0Q0 (W) RW Rent 200 225 112.5 45 9000 1012500 Food 300 350 116.66 20 6000 699960 Clothing 150 175 116.66 8 1200 139992 Fuel 100 110 110 10 1000 110000 Misc. 200 250 125 17 3400 425000 Î£W= 20600 Î£WI = 2387452

The consumer price index for the current year as per family budget method is:

$$\begin{array}{l}\frac{\sum WI}{\sum W} = \frac{2387452}{20600} = 115.89\end{array}$$

Question 5

Arrange an index for 2015 taking 2010 using a simple aggregate and price relatives method

 Items A B C D Year 2010 Price 20 40 50 70 Year 2015 Price 30 50 70 90

Simple Aggregate Method

 Items 2010 Price (P0) 2015 Price (P1) A B C D 20 40 50 70 30 50 70 90 Î£P0Â = 180 Î£P1Â = 240

=Â  240/180Â Ã— 100

= 133.33

Price Relative Method

 Items Year 2010 Price (P0) Year 2015 Price (P1) $$\begin{array}{l}R \,=\, \frac{P_{1}}{P_{0}} \, \times \, 100\end{array}$$ A 20 30 150 B 40 50 125 C 50 70 140 D 70 90 128.57 N= 4 Â Â  = 543.57

Simple Average of Price Relatives

P01 = 543.57/ 4

= 135.89

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