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