Parents can use Class 11 ISC Maths OP Malhotra Solutions Chapter 30 Index Numbers Chapter Test to provide additional support to their children.

## S Chand Class 11 ICSE Maths Solutions Chapter 30 Index Numbers Chapter Test

Question 1.
Construct the consumer price index number for 1990 , taking 1989 as the base year and using simple average of price relative method for the following data :

 Commodities Price in 1989 Price in 1990 Butter 20 21 Cheese 16 12 Milk 3 3 Egg 2.80 2.80

Solution:
We construct the table of values as under:

using simple average of price relatives method
required index number = P01 = $$\frac{1}{\mathrm{~N}} \Sigma\left(\frac{\mathrm{P}_1}{\mathrm{P}_0} \times 100\right)$$ = $$\frac{1}{4} \times 380$$ = 95

Question 2.
A small industrial concern used three raw materials A, B and C in the manufacturing process, the prices of the materials was as shown below :

 Commodity Price (in ₹) in the year 1995 Price (in ₹) in the year 2005 A 4 5 B 60 57 C 36 42

Using 1995 as the base year, calculate a simple aggregate price index for 2005.
Solution:
We construct the following table as under :

By simple aggregate method, we have
required price index for 2015 = P01 = $$\frac{\Sigma \mathrm{P}_1}{\Sigma \mathrm{P}_0} \times 100$$ = $$\frac{104}{100} \times 100$$ = 104

Question 3.
Find the consumer price index number for the year 2010 as the base year by using method of weighted aggregates.

 Commodity A B C D E Year 2000 price (in ₹) per unit 16 40 0.50 5.12 2.00 Year 2010 price (in ₹) per unit 20 60 0.50 6.25 1.50 weights 40 25 5.00 20.00 10.00

Solution:
We construct the table of values as under:

Thus by weighted aggregate method,
required index number = $$\frac{\Sigma \mathrm{P}_1 w}{\Sigma \mathrm{P}_0 w} \times 100$$ = $$\frac{2442.5}{1764.9} \times 100$$ = 138.39

Question 4.
The price of six different commodities for years 2009 and year 2011 are as follows :

 Commodities A B C D E F Price in 2009 (₹) 35 80 25 30 80 x Price in 2011 (₹) 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 125. Find the values of x and y if the total price in 2009 is ₹ 360.
Solution:
We construct the table of values given as under :

 Commodities Price in 2009 p0 Price in 2011 p1 A 35 50 B 80 Y C 25 45 D 30 70 E 80 120 F x 105 Σp0 = 250 + x Σp1 = 390 + y

Since total price in 2009 = ₹ 360 ⇒ 250 + x = 360 ⇒ x = 110
Using simple aggregate method, index number = $$\frac{\Sigma \mathrm{P}_1}{\Sigma \mathrm{P}_0} \times 100$$
⇒ 125 = $$\frac{390+y}{360} \times 100$$
$$\frac{125 \times 36}{10}$$ = 390 + y
⇒ 390 + y = 450
⇒ y = 60