GATE2019 EC: GA-7

Question

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 ______.

• A. $30.43$
• B. $33.43$
• C. $34.43$
• D. $35.43$

Answer 1

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.

Comments

Nice shortcuts

Answer 2

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

 

Comments

Pictorial representation of the answer given..