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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

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:

A. 1 : 3

B. 2 : 5

C. 3 : 7

D. 4 : 9

Solution:

For state Q:
Male population below poverty line = 2.4 million
Let the female population below poverty line be

x

million
Then,

\begin{aligned} 3 : 5 = 2.4 : x \\ \Rightarrow x = \frac{5 \times 2.4}{3} \\ \Rightarrow x = 4 \end{aligned}

∴ Total population below poverty line
= (2.4 + 4) million
= 6.4 million
Let the total population of Q be

p

Then,

\begin{aligned} 25 % of p = 6.4 million \\ \Rightarrow \frac{25}{100} \times p = 6.4 \\ \Rightarrow p = 6.4 \times 4 \\ \Rightarrow p = 25.6 million \end{aligned}

For state T:
Male population below poverty line = 6 million
Let the female population below poverty line be

y

million
Then,

\begin{aligned} 5 : 3 = 6 : y \\ \Rightarrow y = \frac{3 \times 6}{5} \\ \Rightarrow y = 3.6 \end{aligned}

∴ Total population below poverty line
= (6 + 3.6) million
= 9.6 million
Let the total population of state T be

q

Then,

\begin{aligned} 15 % of q = 9.6 million \\ \Rightarrow \frac{15}{100} \times q = 9.6 \\ \Rightarrow q = 9.6 \times \frac{20}{3} \\ \Rightarrow q = 64 million \\ ∴ Required ratio \\ = \frac{p}{q} \\ = \frac{25.6}{64} \\ = 0.4 \\ = \frac{4}{10} \\ = \frac{2}{5} \\ = 2 : 5 \\ So, the ratio of Q : T = 2 : 5 \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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