In a city 68% of population are literates in which the ratio of male to female is 11:6 the ratio of literate females to illiterate females is 8 : 5. Find the total female in the city if total number of male in city is 15250?

Options

A. 9750
B. 10400
C. 9250
D. 8450

Answer

To solve the problem step by step, we will follow the information given in the question and apply the ratios and percentages accordingly.

### Step 1: Determine the total population
Given that the ratio of males to females is 11:6, we can denote the total population as \(100x\), where \(x\) is a common multiplier.

### Step 2: Calculate the number of males
We know the total number of males in the city is 15,250. According to the ratio of males to females (11:6), we can express the number of males as:
\[ \text{Number of males} = \frac{11}{11 + 6} \times \text{Total Population} = \frac{11}{17} \times 100x \]
Setting this equal to the given number of males:
\[ \frac{11}{17} \times 100x = 15250 \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ 100x = 15250 \times \frac{17}{11} \]
Calculating the right side:
\[ 100x = 15250 \times 1.545454545 \approx 23500 \]
Now divide by 100:
\[ x = 235 \]

### Step 4: Calculate the total population
Now that we have \(x\), we can find the total population:
\[ \text{Total Population} = 100x = 100 \times 235 = 23500 \]

### Step 5: Calculate the total number of females
Using the total population, we can find the number of females:
\[ \text{Number of females} = \text{Total Population} - \text{Number of males} = 23500 - 15250 = 8250 \]

### Step 6: Verify the ratios of literate and illiterate females
The ratio of literate females to illiterate females is given as 8:5. Let the number of literate females be \(8y\) and the number of illiterate females be \(5y\). Thus:
\[ 8y + 5y = 8250 \]
\[ 13y = 8250 \implies y = \frac{8250}{13} = 634.615 \text{ (approximately)} \]

### Step 7: Calculate total females
Now substituting back to find the number of literate and illiterate females:
- Literate females = \(8y = 8 \times 634.615 \approx 5076.92\)
- Illiterate females = \(5y = 5 \times 634.615 \approx 3173.08\)

### Final Answer
The total number of females in the city is approximately 8250.