Answer: Option D

Let the total population of state R be x million.
Then, population of state R above poverty line
= [(100 - 24)% of x] million
= $$\left(\frac{76}{100}\times x\right)$$   million
And so, male population of state R above poverty line
$$\left\{ \frac{2}{5}\times\left(\frac{76}{100}\times x\right)\right\}$$    million
But, it is given that male population of state R above poverty line = 1.9 million
$$\eqalign{ & \therefore \frac{2}{5}\times\left(\frac{76}{100}\times x\right) = 1.9 \cr & \Rightarrow x = \frac{5\times100\times1.9}{76\times2} \cr & \Rightarrow x = 6.25 \cr} $$
∴ Total population of state R = 6.25 million

Answer: Option B

For state Q:
Male population below poverty line = 2.4 million
Let the female population below poverty line be $$x$$ million
Then,
$$\eqalign{ & 3 : 5 = 2.4 : x \cr & \Rightarrow x = \frac{5 \times 2.4}{3} \cr & \Rightarrow x = 4 \cr} $$
∴ Total population below poverty line
= (2.4 + 4) million
= 6.4 million
Let the total population of Q be $$p$$
Then,
$$\eqalign{ & 25\% \text{ of }p = 6.4 \text{ million} \cr & \Rightarrow \frac{25}{100}\times p = 6.4 \cr & \Rightarrow p = 6.4\times4 \cr & \Rightarrow p = 25.6 \text{ million} \cr} $$

For state T:
Male population below poverty line = 6 million
Let the female population below poverty line be $$y$$ million
Then,
$$\eqalign{ & 5 : 3 = 6 : y \cr & \Rightarrow y = \frac{3\times6}{5} \cr & \Rightarrow y = 3.6 \cr} $$
∴ Total population below poverty line
= (6 + 3.6) million
= 9.6 million
Let the total population of state T be $$q$$
Then,
$$\eqalign{ & 15\% \text{ of } q = 9.6 \text{ million} \cr & \Rightarrow \frac{15}{100} \times q = 9.6 \cr & \Rightarrow q = 9.6\times \frac{20}{3} \cr & \Rightarrow q = 64 \text{ million} \cr & \therefore \text{Required ratio} \cr & = \frac{p}{q} \cr & = \frac{25.6}{64} \cr & = 0.4 \cr & = \frac{4}{10} \cr & = \frac{2}{5} \cr & = 2 : 5 \cr & \text{So, the ratio of } \text{Q}:\text{T} = 2:5 \cr} $$

Answer: Option B

Total population of state S = 7 million
∴ Population above poverty line
= {(100 - 19)% of 7} million
= (81% of 7) million
= 5.67 million
And so, the number of females above poverty line in state S
$$\eqalign{ & = \left(\frac{3}{7}\times5.67\right) \text{million} \cr & = 2.43 \text{ million} \cr} $$

Answer: Option D

Female population below poverty line for state P = 2.1 million.
Let the male population below poverty line for state P be x million.
Then,
$$\eqalign{ & 5:6 = x:2.1 \cr & \Rightarrow \frac{x}{2.1} = \frac{5}{6} \cr & \Rightarrow x = \frac{2.1\times5}{6} \cr & \Rightarrow x = 1.75 \cr} $$
∴ Population below poverty line for state P
= (2.1 + 1.75) million
= 3.85 million
Let the population above poverty line for state P be y million.
Since, 35% of the total population of state P is below poverty line, therefore 65% of the total population of state P is above poverty line. So, the ratio of population below poverty line to that above poverty line for state P is 35 : 65.
$$\eqalign{ & \therefore 35 : 65 = 3.85 : y \cr & \Rightarrow y = \frac{65\times3.85}{35} \cr & \Rightarrow y = 7.15 \cr} $$
∴ Population above poverty line for state P = 7.15 million and so, male population above poverty line for state P
$$\eqalign{ & = \left(\frac{6}{13}\times 7.15\right) \text{million} \cr & = 3.3 \text{ million} \cr} $$