Understanding the Data Table on State Population and Poverty

The question asks us to find the ratio of the total population of State 'B' to the total population of State 'E'. We are given specific information about the population of males below the poverty line for both states and a data table detailing population distribution based on poverty line and gender ratios for five states, including B and E.

Let's first look at the relevant parts of the provided data table for states B and E:

We are also given:

• Population of males below poverty line for state ‘B’ = 2.4 million.
• Population of males below poverty line for state ‘E’ = 6 million.

To find the ratio of the total populations of State B and State E, we need to calculate the total population for each state individually.

Calculating Total Population for State B

We know the population of males below the poverty line (BPL) in State B is 2.4 million. The table shows that the ratio of males to females BPL in State B is 3 ∶ 5. This means for every 3 males BPL, there are 5 females BPL.

• Let the population of males BPL in State B be $M_{BPL,B}$. $M_{BPL,B} = 2.4$ million.
• The ratio $M_{BPL,B} : F_{BPL,B} = 3 : 5$.
• We can represent the male BPL population as 3 'parts' and the female BPL population as 5 'parts'.
• So, 3 parts = 2.4 million.
• 1 part = $\frac{2.4}{3} = 0.8$ million.
• The total population BPL in State B is the sum of male and female populations BPL, which is $3 + 5 = 8$ parts.
• Total population BPL in State B = 8 parts × 0.8 million/part = $8 \times 0.8 = 6.4$ million.

Now we use the information about the percentage of population below the poverty line. For State B, 25% of the total population is BPL. Let $P_B$ be the total population of State B.

• 25% of $P_B$ = Total population BPL in State B
• $0.25 \times P_B = 6.4$ million
• $P_B = \frac{6.4}{0.25} = \frac{6.4}{\frac{1}{4}} = 6.4 \times 4 = 25.6$ million.

So, the total population of State B is 25.6 million.

Calculating Total Population for State E

We know the population of males below the poverty line (BPL) in State E is 6 million. The table shows that the ratio of males to females BPL in State E is 5 ∶ 3. This means for every 5 males BPL, there are 3 females BPL.

• Let the population of males BPL in State E be $M_{BPL,E}$. $M_{BPL,E} = 6$ million.
• The ratio $M_{BPL,E} : F_{BPL,E} = 5 : 3$.
• We can represent the male BPL population as 5 'parts' and the female BPL population as 3 'parts'.
• So, 5 parts = 6 million.
• 1 part = $\frac{6}{5} = 1.2$ million.
• The total population BPL in State E is the sum of male and female populations BPL, which is $5 + 3 = 8$ parts.
• Total population BPL in State E = 8 parts × 1.2 million/part = $8 \times 1.2 = 9.6$ million.

Now we use the information about the percentage of population below the poverty line. For State E, 15% of the total population is BPL. Let $P_E$ be the total population of State E.

• 15% of $P_E$ = Total population BPL in State E
• $0.15 \times P_E = 9.6$ million
• $P_E = \frac{9.6}{0.15} = \frac{9.6}{\frac{15}{100}} = \frac{9.6 \times 100}{15} = \frac{960}{15}$.
• $\frac{960}{15} = \frac{192 \times 5}{3 \times 5} = \frac{192}{3} = 64$ million.

So, the total population of State E is 64 million.

Finding the Ratio of Total Populations

We need to find the ratio of the total population of State B to the total population of State E, which is $P_B : P_E$.

• Ratio = 25.6 million : 64 million.
• To simplify the ratio, we can write it as a fraction: $\frac{25.6}{64}$.
• Multiply the numerator and denominator by 10 to remove the decimal: $\frac{256}{640}$.
• Now, we can simplify this fraction. Both 256 and 640 are divisible by 64.
• $256 \div 64 = 4$.
• $640 \div 64 = 10$.
• The ratio is $\frac{4}{10}$.
• Simplify further by dividing by 2: $\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$.

The ratio of the total population of State B to State E is 2 : 5.

Based on our calculations, the ratio of the total population of states ‘B’ and ‘E’ is 2 ∶ 5.

Revision Table: Key Calculations

Additional Information: Data Interpretation Basics

Data interpretation questions often involve analyzing tables or charts to extract relevant information and perform calculations. Key skills needed include:

• Carefully reading the question and understanding what is being asked.
• Identifying the specific data points needed from the table or chart.
• Understanding percentages, ratios, and proportions.
• Setting up equations based on the given information.
• Performing arithmetic calculations accurately.
• Simplifying ratios or fractions to their lowest terms.

In this question, we used the male population BPL and the BPL gender ratio to find the total BPL population. Then, we used the percentage of total population that is BPL to work backward and find the overall total population for each state. Finally, we calculated the required ratio.