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GATE ECE 2019 | GA | Question: 7

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The bar graph in panel (a) shows the proportion of male and female illiterates in $2001$ and $2011.$ The proportions of males and females in $2001$ and $2011$ are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of literates from $2001$ to $2011$ is ______.

 

  1. $30.43$
  2. $33.43$
  3. $34.43$
  4. $35.43$

3 Answers

Best answer
21 21 votes

The graph is for illiterates. 

  • Percentage of male literates in $2011 =100-40=60$
  • Percentage of male literates in $2001 =100- 50=50$
  • Percentage of female literates in $2011 =100-40=60$
  • Percentage of female literates in $2001 =100- 60=40$

Let $X$ be the total population (This remains same in $2001$ and $2011$ as per question)

Number of literates in $2011 = 0.5 \times 0.6 \times X + 0.5 \times 0.6 \times X = 0.6 X$

Number of literates in $2001 = 0.6 \times 0.5 \times X + 0.4 \times 0.4 \times X = 0.46 X$

So, percentage increase in the literates $ = \dfrac{0.6X - 0.46X}{0.46X} \times {100\%} = \dfrac{700}{23}=30.43$

Option A.

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Let us consider total no of population is 100.

It is given total population doesn't change remain same both years.

in 2001

no of male=60

Literate male= 50%of 60=30

No of females= 40

Literate females= 40% of 40=16

So total literate in 2001=30+16=46

in 2011

no of male are 50% so 50

Literate male= 60% of 50= 30

No of females= 50

Literate females= 60%of 50=30

So total literate in 2011= 30+30=60

percentage change in literate population from 2001 to 2011

=( Total literate in 2011-total literate in 2001)*100/total literate in 2001

=( 60-46)*100/46= 1400/46= 30.43%

Answer A

 

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Assume total population = 100 (since it stays constant).

2001

  • Male = 60, Female = 40
  • Illiterate:
    • Male = 50% → Literate = 50% of 60 = 30
    • Female = 60% → Literate = 40% of 40 = 16
  • Total literates (2001) = 30 + 16 = 46

2011

  • Male = 50, Female = 50
  • Illiterate = 40% for both → Literate = 60%
    • Male literates = 60% of 50 = 30
    • Female literates = 60% of 50 = 30
  • Total literates (2011) = 60

Percentage increase

=(60-46)/46=30.43

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