Revision and Self Assessment on Index Numbers Class 11 OP Malhotra Exe-30C ISC Maths Solutions Ch-30. In this article you would learn to solve conceptional problems easily on Index Numbers. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11.

Index Numbers Class 11 OP Malhotra Revision and Self Assessment ISC Maths Solutions Ch-30

Board	ICSE
Publications	S Chand
Subject	Maths
Class	11th
Chapter-30	Index Numbers
Writer	OP Malhotra
Exe-30(C)	Revision and Self Assessment.

Revision and Self Assessment on Index Numbers

OP Malhotra ISC Class 11 Maths Solutions

Que-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

 

Sol:  We use the formula of simple average of price relatives:
Price Relative (P) = (Price in current year / Price in base year) × 100
Now calculate for each commodity:
Butter: (21 / 20) × 100 = 105
Cheese: (12 / 16) × 100 = 75
Milk: (3 / 3) × 100 = 100
Egg: (2.80 / 2.80) × 100 = 100
Now take average:
CPI = (105 + 75 + 100 + 100) / 4
= 380 / 4 = 95
Hence, Consumer Price Index for 1990 = 95

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

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

Using 1995 as the base year, calculate a simple aggregate price index for 2005.

Sol: We use the simple aggregate price index formula:
Price Index = (ΣP₁ / ΣP₀) × 100
Where:
P₀ = Price in base year (1995)
P₁ = Price in current year (2005)
Now calculate sums:
ΣP₀ = 4 + 60 + 36 = 100
ΣP₁ = 5 + 57 + 42 = 104
Now substitute:
Price Index = (104 / 100) × 100 = 104
Hence, Simple Aggregate Price Index for 2005 = 104

Que-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 (₹) per unit	16	40	0.50	5.12	2.00
Year 2010 price (₹) per unit	20	60	0.50	6.25	1.50
Weights	40	25	5.00	20.00	10.00

 

Sol: We are given data for base year (2000) and current year (2010) along with weights.
We need to find Consumer Price Index (CPI) using Weighted Aggregative Method.
Formula:
CPI = (Σ W × P₁ / Σ W × P₀) × 100
Where,
P₀ = Price in base year (2000)
P₁ = Price in current year (2010)
W = Weights
Now calculate W × P₀ and W × P₁:

Commodity	W	P₀	P₁	W × P₀	W × P₁
A	40	16	20	640	800
B	25	40	60	1000	1500
C	5	0.50	0.50	2.5	2.5
D	20	5.12	6.25	102.4	125
E	10	2.00	1.50	20	15
Total				1764.9	2442.5

Now apply formula : CPI = (2442.5 / 1764.9) × 100
CPI ≈ 138.36
Hence, the Consumer Price Index Number for the year 2010 (base year 2000) is approximately 138.36.

Que-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.

Sol: Given:
ΣP₀ (total price in 2009) = 360
From table:
35 + 80 + 25 + 30 + 80 + x = 360
250 + x = 360
x = 360 − 250 = 110
Now use Index Number formula:
Index Number = (ΣP₁ / ΣP₀) × 100
Given Index Number = 125
So,
125 = (ΣP₁ / 360) × 100
ΣP₁ = (125 × 360) / 100 = 450
Now find ΣP₁ using table:
50 + y + 45 + 70 + 120 + 105 = 450
(390 + y) = 450
y = 450 − 390 = 60
Hence, the values are:
x = 110 and y = 60

–: End Index Numbers Class 11 OP Malhotra Exe-30C ISC Maths Ch-30 Solutions :–

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