Understanding Population Break-up Data

The question asks us to compare the female population in City 'C' with the combined male and transgender population in City 'D' based on the provided table. The table shows population data for five cities, with some values given as percentages and others as absolute numbers.

To solve this, we first need to determine the actual number of females in City 'C' and the actual number of males and transgenders in City 'D'.

Calculating Population for City C

For City 'C', we are given the number of males (8000) and the percentages of females (35%) and transgenders (15%). The total percentage for all categories must sum up to 100%.

• Percentage of Females in C = 35%
• Percentage of Transgenders in C = 15%
• Combined percentage of Females and Transgenders in C = \(35\% + 15\% = 50\%\)

The remaining percentage must be for males. So, the percentage of males in C is \(100\% - 50\% = 50\%\).

We know that 50% of the total population of City C is 8000 males.

Let the total population of City C be \(P_C\).

\(50\%\) of \(P_C = 8000\)

\(\frac{50}{100} \times P_C = 8000\)

\(0.5 \times P_C = 8000\)

\(P_C = \frac{8000}{0.5} = 16000\)

The total population of City C is 16000.

Now we can find the number of females in City C:

Female population in City C = \(35\%\) of \(P_C\)

Female population in City C = \(\frac{35}{100} \times 16000\)

Female population in City C = \(0.35 \times 16000 = 5600\)

So, the female population in City 'C' is 5600.

Calculating Population for City D

For City 'D', we are given the number of females (3600) and the percentages of males (45%) and transgenders (25%).

• Percentage of Males in D = 45%
• Percentage of Transgenders in D = 25%
• Percentage of Females in D = 100% - (Percentage of Males + Percentage of Transgenders)
• Percentage of Females in D = \(100\% - (45\% + 25\%)\)
• Percentage of Females in D = \(100\% - 70\% = 30\%\)

We know that 30% of the total population of City D is 3600 females.

Let the total population of City D be \(P_D\).

\(30\%\) of \(P_D = 3600\)

\(\frac{30}{100} \times P_D = 3600\)

\(0.30 \times P_D = 3600\)

\(P_D = \frac{3600}{0.30} = 12000\)

The total population of City D is 12000.

Now we need to find the number of males and transgenders in City D:

Male population in City D = \(45\%\) of \(P_D\)

Male population in City D = \(\frac{45}{100} \times 12000\)

Male population in City D = \(0.45 \times 12000 = 5400\)

Transgender population in City D = \(25\%\) of \(P_D\)

Transgender population in City D = \(\frac{25}{100} \times 12000\)

Transgender population in City D = \(0.25 \times 12000 = 3000\)

Sum of male and transgender population in City D = Male population in D + Transgender population in D

Sum of male and transgender population in City D = \(5400 + 3000 = 8400\)

Calculating Percentage Difference

The question asks: Female population in City 'C' is how much percent less than the sum of male and transgender population of City 'D'?

• Female population in City C = 5600
• Sum of male and transgender population in City D = 8400

The difference between the sum of male and transgender population in City D and the female population in City C is:

Difference = Sum of male and transgender population in D - Female population in C

Difference = \(8400 - 5600 = 2800\)

To find out how much percent less the female population in City C is compared to the sum of male and transgender population in City D, we use the formula:

Percentage Less = \(\frac{\text{Difference}}{\text{Base Value}} \times 100\)

Here, the base value is the sum of male and transgender population in City D, which is 8400.

Percentage Less = \(\frac{2800}{8400} \times 100\)

Percentage Less = \(\frac{28}{84} \times 100\)

Simplify the fraction \(\frac{28}{84}\) by dividing both numerator and denominator by their greatest common divisor, which is 28.

\(\frac{28 \div 28}{84 \div 28} = \frac{1}{3}\)

Percentage Less = \(\frac{1}{3} \times 100 = \frac{100}{3} \% = 33\frac{1}{3} \% \)

So, the female population in City 'C' is \(33\frac{1}{3} \%\) less than the sum of male and transgender population of City 'D'.

Revision Table: Population Summary

Additional Information: Percentage Change Calculation

When comparing two values, say Value A and Value B, we often need to find the percentage difference or percentage change. The formula depends on whether you are calculating "percent less than" or "percent more than", and which value is used as the base.

• Percent Less Than: If Value A is less than Value B, the percentage by which A is less than B is calculated as \(\frac{\text{Value B} - \text{Value A}}{\text{Value B}} \times 100\). Here, Value B is the base.
• Percent More Than: If Value A is more than Value B, the percentage by which A is more than B is calculated as \(\frac{\text{Value A} - \text{Value B}}{\text{Value B}} \times 100\). Here, Value B is also the base.
• Percentage Change: If a value changes from an Initial Value to a Final Value, the percentage change is \(\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\). If the result is positive, it's a percentage increase; if negative, it's a percentage decrease.

In this problem, we were asked for the percentage by which the female population in City C (Value A = 5600) is less than the sum of male and transgender population in City D (Value B = 8400). Therefore, we used Value B as the base for calculation, which aligns with the "Percent Less Than" formula.