District Population Literacy Analysis

This problem involves calculating the percentage of literate females in a district's population. We are given the total population, the number of males, the overall literacy percentage, and the male literacy percentage. We need to determine the female literacy percentage.

Step 1: Understand the Given Data

• Total Population: $328000$
• Number of Males: $164000$
• Percentage of Literate Population: $24\%$
• Percentage of Literate Males: $34\%$

Female Population Calculation

First, we find the number of females in the district. This is done by subtracting the number of males from the total population.

$ \text{Number of Females} = \text{Total Population} - \text{Number of Males} $

$ \text{Number of Females} = 328000 - 164000 = 164000 $

There are $164000$ females in the district.

Total Literate Population Calculation

Next, we calculate the total number of literate people in the district using the overall literacy rate.

$ \text{Total Literate Population} = \frac{24}{100} \times \text{Total Population} $

$ \text{Total Literate Population} = 0.24 \times 328000 = 78720 $

A total of $78720$ people are literate in the district.

Literate Male Count Calculation

Now, we determine the number of literate males based on the percentage of literate males.

$ \text{Number of Literate Males} = \frac{34}{100} \times \text{Number of Males} $

$ \text{Number of Literate Males} = 0.34 \times 164000 = 55760 $

So, $55760$ males are literate.

Literate Female Count Calculation

We can find the number of literate females by subtracting the number of literate males from the total literate population.

$ \text{Number of Literate Females} = \text{Total Literate Population} - \text{Number of Literate Males} $

$ \text{Number of Literate Females} = 78720 - 55760 = 22960 $

There are $22960$ literate females.

Female Literacy Percentage Calculation

Finally, we calculate the percentage of females who are literate. We divide the number of literate females by the total number of females and multiply by 100.

$ \text{Percentage of Literate Females} = \left( \frac{\text{Number of Literate Females}}{\text{Number of Females}} \right) \times 100 $

$ \text{Percentage of Literate Females} = \left( \frac{22960}{164000} \right) \times 100 $

$ \text{Percentage of Literate Females} = 0.14 \times 100 = 14\% $

The percentage of literate females in the district is $14\%$.