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1. The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.

State Percentage of Population Below Poverty Line Proportion of Males and Females

Below Poverty Line Above Poverty Line

M : F F : F

P 35 5 : 6 6 : 7

Q 25 3 : 5 4 : 5

R 24 1 : 2 2 : 3

S 19 3 : 2 4 : 3

T 15 5 : 3 3 : 2

What will be the male population above poverty line for State P if the female population below poverty line for State P is 2.1 million?

A. 2.1 million

B. 2.3 million

C. 2.7 million

D. 3.3 million

Solution:

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,

\begin{aligned} 5 : 6 = x : 2.1 \\ \Rightarrow \frac{x}{2.1} = \frac{5}{6} \\ \Rightarrow x = \frac{2.1 \times 5}{6} \\ \Rightarrow x = 1.75 \end{aligned}

∴ 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.

\begin{aligned} ∴ 35 : 65 = 3.85 : y \\ \Rightarrow y = \frac{65 \times 3.85}{35} \\ \Rightarrow y = 7.15 \end{aligned}

∴ Population above poverty line for state P = 7.15 million and so, male population above poverty line for state P

\begin{aligned} = (\frac{6}{13} \times 7.15) million \\ = 3.3 million \end{aligned}

State	Percentage of Population Below Poverty Line	Proportion of Males and Females
		Below Poverty Line	Above Poverty Line
		M : F	F : F
P	35	5 : 6	6 : 7
Q	25	3 : 5	4 : 5
R	24	1 : 2	2 : 3
S	19	3 : 2	4 : 3
T	15	5 : 3	3 : 2

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