Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

From the following data calculate Price index number using ($i$) 2010 as the base ($ii$) 2013 as the base ($iii$) 2010 to 2012 as the base

Year

2010

2011

2012

2013

2014

2015

2016

Prices (₹)

50

53

32

40

46

41

42

Options:

(i) 80.0, (ii) 100.0, (iii) 88.9

(i) 84.0, (ii) 105.0, (iii) 93.3

(i) 92.0, (ii) 115.0, (iii) 102.2

(i) 106.0, (ii) 132.5, (iii) 117.8

Correct Answer:

(i) 84.0, (ii) 105.0, (iii) 93.3

Explanation:

The correct answer is Option (2) → (i) 84.0, (ii) 105.0, (iii) 93.3

$\text{*Mean of prices from 2010 to 2012} = \frac{50 + 53 + 32}{3} = \frac{135}{3} = 45$

Year

Prices (₹)

Index Nos. (Base = 2010)

Index Nos. (Base = 2013)

*Index Nos. (Base = 2010 to 2012 i.e., 45)

2010

50

100

$\frac{50 \times 100}{40} = 125.0$

$\frac{50 \times 100}{45} = 111.11$

2011

53

$\frac{53 \times 100}{50} = 106$

$\frac{53 \times 100}{40} = 132.5$

$\frac{53 \times 100}{45} = 117.78$

2012

32

$\frac{32 \times 100}{50} = 64$

$\frac{32 \times 100}{40} = 80.0$

$\frac{32 \times 100}{45} = 71.11$

2013

40

$\frac{40 \times 100}{50} = 80$

100

$\frac{40 \times 100}{45} = 88.89$

2014

46

$\frac{46 \times 100}{50} = 92$

$\frac{46 \times 100}{40} = 115.0$

$\frac{46 \times 100}{45} = 102.22$

2015

41

$\frac{41 \times 100}{50} = 82$

$\frac{41 \times 100}{40} = 102.5$

$\frac{41 \times 100}{45} = 91.11$

2016

42

$\frac{42 \times 100}{50} = 84$

$\frac{42 \times 100}{40} = 105.0$

$\frac{42 \times 100}{45} = 93.33$