Solving Population Data Interpretation Question

This problem requires us to analyze the provided table showing village-wise population distribution by gender (Male, Female, Transgender). Some percentage values are missing, and we need to calculate them first before answering the question about the number of females in Villages B and D compared to males in Village C.

Understanding the Population Distribution Table

The table gives the total population for five villages (A to E) and the percentage distribution of males (M), females (F), and transgenders (T) within each village. For any given village, the percentages of M, F, and T must add up to 100%.

Calculating Missing Percentage Values

We can find the missing percentages using the fact that M% + F% + T% = 100% for each village.

• Village A: F% = 100% - M% - T% = \(100\% - 46\% - 22\% = 32\%\)
• Village B: M% = 100% - F% - T% = \(100\% - 33\% - 27\% = 40\%\)
• Village C: T% = 100% - M% - F% = \(100\% - 32\% - 36\% = 32\%\)
• Village D: F% = 100% - M% - T% = \(100\% - 36\% - 20\% = 44\%\)
• Village E: M% = 100% - F% - T% = \(100\% - 30\% - 25\% = 45\%\)

Here is the completed table with all percentages:

Calculating Number of Females in Villages B and D

• Females in Village B: Population of Village B = 16,000 Percentage of females in Village B = 33% Number of females in Village B = \(33\% \text{ of } 16,000 = \frac{33}{100} \times 16,000\)

\( = 33 \times 160 = 5,280\)

• Females in Village D: Population of Village D = 24,000 Percentage of females in Village D = 44% (calculated) Number of females in Village D = \(44\% \text{ of } 24,000 = \frac{44}{100} \times 24,000\)

\( = 44 \times 240 = 10,560\)

• Total Females in Villages B and D together: Total Females (B+D) = Females in B + Females in D Total Females (B+D) = \(5,280 + 10,560 = 15,840\)

Calculating Number of Males in Village C

• Males in Village C: Population of Village C = 18,000 Percentage of males in Village C = 32% Number of males in Village C = \(32\% \text{ of } 18,000 = \frac{32}{100} \times 18,000\)

\( = 32 \times 180 = 5,760\)

Calculating Percentage More

We need to find the percentage by which the total number of females in Villages B and D together (15,840) is more than the number of males in Village C (5,760).

The formula for percentage more is:

\(\text{Percentage More} = \frac{(\text{Value A} - \text{Value B})}{\text{Value B}} \times 100\%\)

Here, Value A = Total Females (B+D) = 15,840, and Value B = Males (C) = 5,760.

\(\text{Percentage More} = \frac{(15,840 - 5,760)}{5,760} \times 100\%\)

\(\text{Percentage More} = \frac{10,080}{5,760} \times 100\%\)

Simplify the fraction:

\(\frac{10,080}{5,760} = \frac{1008}{576}\)

Divide numerator and denominator by common factors (e.g., 8, then 9, then 2):

\(\frac{1008 \div 8}{576 \div 8} = \frac{126}{72}\)

\(\frac{126 \div 9}{72 \div 9} = \frac{14}{8}\)

\(\frac{14 \div 2}{8 \div 2} = \frac{7}{4}\)

Now substitute this back into the percentage formula:

\(\text{Percentage More} = \frac{7}{4} \times 100\%\)

\(\text{Percentage More} = 1.75 \times 100\%\)

\(\text{Percentage More} = 175\%\)

Therefore, the total number of females in Villages B and D together is 175% more than the number of males in Village C.

Revision Table: Key Calculations

Additional Information on Percentage Calculations

Understanding percentages and how to calculate percentage differences is crucial for data interpretation questions. A percentage is a fraction of 100. To find a percentage of a number, you convert the percentage to a decimal or a fraction and multiply it by the number.

• To calculate X% of a number N: \(\frac{X}{100} \times N\)

When comparing two values, A and B, to find the percentage by which A is more than B, we use the formula:

\(\text{Percentage More} = \frac{(\text{Difference between A and B})}{\text{Original Value (B)}} \times 100\%\)

Or, specifically when A > B:

\(\text{Percentage More} = \frac{(A - B)}{B} \times 100\%\)

If A < B, and you want to find the percentage by which A is less than B, the formula is:

\(\text{Percentage Less} = \frac{(B - A)}{B} \times 100\%\)

These calculations help in understanding the relative differences between quantities based on given data, as demonstrated in this population distribution problem.