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 = P_{01} = \(\frac{1}{\mathrm{~N}} \Sigma\left(\frac{\mathrm{P}_1}{\mathrm{P}_0} \times 100\right)\) = \(\frac{1}{4} \times 380\) = 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 = P_{01} = \(\frac{\Sigma \mathrm{P}_1}{\Sigma \mathrm{P}_0} \times 100\) = \(\frac{104}{100} \times 100\) = 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 p_{0} | Price in 2011 p_{1} |

A | 35 | 50 |

B | 80 | Y |

C | 25 | 45 |

D | 30 | 70 |

E | 80 | 120 |

F | x | 105 |

Σp_{0} = 250 + x | Σp_{1} = 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