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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

From the data given below, calculate price Index numbers by taking ($i$) 2005 as base year, ($ii$) 2014 as base year, ($iii$) 2009 to 2011 as base.

Year:

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

Price:

5

7

10

12

11

10

9

15

18

20
Options:

(i) 350, (ii) 90, (iii) 180

(i) 400, (ii) 100, (iii) 200

(i) 420, (ii) 110, (iii) 210

(i) 380, (ii) 95, (iii) 190

Correct Answer:

(i) 400, (ii) 100, (iii) 200

Explanation:

The correct answer is Option (2) → (i) 400, (ii) 100, (iii) 200

$\text{Arithmetic Mean of prices from 2009 to 2011} = \frac{11+10+9}{3} = 10 \text{}$

Year

Price

Price Indices (2005 as base)

Price Indices (2014 as base)

Price Indices base from 2009 to 2011

2005

5

100

$\frac{500}{20} = 25$

$\frac{500}{10} = 50$

2006

7

$\frac{700}{5} = 140$

$\frac{700}{20} = 35$

$\frac{700}{10} = 70$

2007

10

$\frac{1000}{5} = 200$

$\frac{1000}{20} = 50$

$\frac{1000}{10} = 100$

2008

12

$\frac{1200}{5} = 240$

$\frac{1200}{20} = 60$

$\frac{1200}{10} = 120$

2009

11

$\frac{1100}{5} = 220$

$\frac{1100}{20} = 55$

$\frac{1100}{10} = 110$

2010

10

$\frac{1000}{5} = 200$

$\frac{1000}{20} = 50$

$\frac{1000}{10} = 100$

2011

9

$\frac{900}{5} = 180$

$\frac{900}{20} = 45$

$\frac{900}{10} = 90$

2012

15

$\frac{1500}{5} = 300$

$\frac{1500}{20} = 75$

$\frac{1500}{10} = 150$

2013

18

$\frac{1800}{5} = 360$

$\frac{1800}{20} = 90$

$\frac{1800}{10} = 180$

2014

20

$\frac{2000}{5} = 400$

100

$\frac{2000}{10} = 200$

 

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