Question

State	Percentage of population below poverty line	Ratio of Male to Female which are below Poverty line	Ratio of Male to Female which are above Poverty line
R	24	1:2	2:3

 If the male population above poverty line for a state R is 1.9 million, then total population of the state is:
(a) 4.5 million
(b) 4.85 million
(c) 5.35 million
(d) 6.25 million

Answer 1

Hint: We have a given percentage of population below poverty line and we are given the male population above poverty line so first of all, we are going to find the percentage of population above poverty line by subtracting the given population from 100. Then let us assume that the total population of state R is x. We have given the ratio of male to female above the poverty line so we are going to take male population from it and divide it by the sum of male and female population. Then we will multiply this fraction with the percentage of population and by x which we have calculated above and equate it to 1.9 million. Solving this equation will give us the value of x which is the total population.

Complete step by step answer:
Let us assume that the total population of state R is x.
Then the population which is above poverty line is equal to subtracting 24 from 100 we get,
$\begin{align}
  & 100-24 \\
 & =76\% \\
\end{align}$
Now, we got the percentage of the population in state R which is above the poverty line as $76\%$.
The number of population in state R is calculated by multiplying 76 by x followed by division of this result of multiplication by 100.
$\dfrac{76}{100}x$
We have also given the ratio of male to female population which is above poverty line are:
$2:3$
So, the fraction of male population among total population is equal to:
$\begin{align}
  & \dfrac{2}{2+3} \\
 & =\dfrac{2}{5} \\
\end{align}$
Now, we are going to multiply this fraction of male population to $\dfrac{76}{100}x$ . We get the number of male population in state R which is above the poverty line.
$\dfrac{76x}{100}\left( \dfrac{2}{5} \right)$
Equating the above expression to the male population which is above poverty line (1.9 million) we get,
$\begin{align}
  & \dfrac{76x}{100}\left( \dfrac{2}{5} \right)=1.9million \\
 & \Rightarrow 152x=1.9\left( 500 \right)million \\
 & \Rightarrow 152x=950million \\
\end{align}$
Dividing 152 on both the sides we get,
$\begin{align}
  & x=\dfrac{950}{152}million \\
 & \Rightarrow x=6.25million \\
\end{align}$
From the above, we got the total population of state R as 6.25 million.

So, the correct answer is “Option D”.

Note: The plausible mistake that could happen in this problem is that, instead of taking the male to female ratio of above poverty line population, you might have taken the male to female ratio of below poverty line. There are two reasons for that:
First is as it is written first in the column then the “above poverty line” ratio of male to female has been written. Other reason is the normal, human error which can be possible when we are in hurry to solve the problem
So, make sure you won’t make this mistake.