If the population of males below poverty line for State Q is 2.4 million and that for State T is 6 million, then the total population of state Q and T are in the ratio:

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,
$$\begin{array}{rl}& 3:5=2.4:x\\ & \Rightarrow x=\frac{5\times 2.4}{3}\\ & \Rightarrow x=4\end{array}$$
∴ Total population below poverty line
= (2.4 + 4) million
= 6.4 million
Let the total population of Q be $$p$$
Then,
$$\begin{array}{rl}& 25\%\text{ of }p=6.4\text{ million}\\ & \Rightarrow \frac{25}{100}\times p=6.4\\ & \Rightarrow p=6.4\times 4\\ & \Rightarrow p=25.6\text{ million}\end{array}$$

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