Understanding the Population Data

The problem provides a table showing the breakdown of population in five different cities (A to E) by gender: males, females, and transgenders. Some data is given as a percentage of the total population, while other data is given as a direct number. We need to use this information to find the ratio of the transgender population in City C to the transgender population in City D.

Calculating Transgender Population for City C

For City C, we are given the number of males and the percentages for females and transgenders. The percentages for females and transgenders are 35% and 15% respectively.

• Percentage of Females + Transgenders in City C = $\text{35%} + \text{15%} = \text{50%}$.
• The remaining percentage must represent the males. So, the percentage of males in City C = $\text{100%} - \text{50%} = \text{50%}$.
• We are given that the number of males in City C is 8000.
• Therefore, 50% of the total population of City C is 8000.
• To find the total population of City C, we can set up the equation: $\text{0.50} \times \text{Total Population}_{\text{C}} = \text{8000}$.
• Total Population of City C = $\frac{\text{8000}}{\text{0.50}} = \text{16000}$.
• Now we can calculate the transgender population in City C, which is 15% of the total population.
• Transgender Population in City C = $\text{15% of 16000} = \text{0.15} \times \text{16000} = \text{2400}$.

Calculating Transgender Population for City D

For City D, we are given the percentage for males and transgenders, and the number for females. The percentages for males and transgenders are 45% and 25% respectively.

• Percentage of Males + Transgenders in City D = $\text{45%} + \text{25%} = \text{70%}$.
• The remaining percentage must represent the females. So, the percentage of females in City D = $\text{100%} - \text{70%} = \text{30%}$.
• We are given that the number of females in City D is 3600.
• Therefore, 30% of the total population of City D is 3600.
• To find the total population of City D, we can set up the equation: $\text{0.30} \times \text{Total Population}_{\text{D}} = \text{3600}$.
• Total Population of City D = $\frac{\text{3600}}{\text{0.30}} = \text{12000}$.
• Now we can calculate the transgender population in City D, which is 25% of the total population.
• Transgender Population in City D = $\text{25% of 12000} = \text{0.25} \times \text{12000} = \text{3000}$.

Finding the Ratio of Transgender Populations

We need to find the ratio of the transgender population of City C to the transgender population of City D.

• Transgender Population of City C = 2400
• Transgender Population of City D = 3000
• Ratio = Transgender Population (C) : Transgender Population (D)
• Ratio = 2400 : 3000
• To simplify the ratio, we can divide both numbers by their greatest common divisor. First, divide by 100: $2400 : 3000 = 24 : 30$.
• Now, divide by 6: $24 : 30 = \frac{24}{6} : \frac{30}{6} = 4 : 5$.

The ratio of the transgender population of City C to the transgender population of City D is $4 : 5$.

Revision Table: Key Calculations

Additional Information: Working with Ratios and Percentages

Data interpretation questions often require converting between numbers and percentages, or calculating ratios. Here are some key concepts:

• Percentage: A percentage is a fraction out of 100. For example, 15% is equivalent to $\frac{15}{100}$ or 0.15.
• Finding the Whole from a Part: If you know that a certain number represents a specific percentage of a total, you can find the total by dividing the number by the percentage (as a decimal). For instance, if 8000 is 50% of the total, Total = $8000 / 0.50$.
• Finding a Part from the Whole: If you know the total and a percentage, you can find the corresponding number by multiplying the total by the percentage (as a decimal). For instance, 15% of 16000 is $0.15 \times 16000$.
• Ratio: A ratio compares two or more quantities. A ratio $a : b$ can be written as a fraction $\frac{a}{b}$. Ratios should usually be simplified to their simplest form by dividing all parts by their greatest common divisor.
• Population Break-up: In population data like this, the percentages of all categories (males, females, transgenders) for a given city must add up to 100%. This fact is crucial for solving problems where one part's percentage is unknown but its number is given.