The total population of a city is `2,40,000` in which `1,32,000` are men. Out of every 100 men there are 90 educated. But over all `64%` people are educated in total population . Find the educated women percentage ?

Options

A. `29(9)/(10)%`
B. `26%`
C. `32(2)/(9)%`
D. `16(1)/(3)%`

Answer

To find the percentage of educated women in the city, we can follow these steps:

### Step 1: Determine the total population of women
The total population of the city is 2,40,000, and the number of men is 1,32,000. To find the number of women, we subtract the number of men from the total population.

\[ \text{Number of women} = \text{Total population} - \text{Number of men} = 2,40,000 - 1,32,000 = 1,08,000 \]

### Step 2: Calculate the number of educated men
Out of every 100 men, 90 are educated. Therefore, to find the number of educated men, we calculate 90% of the total number of men.

\[ \text{Number of educated men} = 90\% \text{ of } 1,32,000 = \frac{90}{100} \times 1,32,000 = 1,18,800 \]

### Step 3: Determine the total number of educated people
We know that 64% of the total population is educated. To find the total number of educated people, we calculate 64% of the total population.

\[ \text{Total educated people} = 64\% \text{ of } 2,40,000 = \frac{64}{100} \times 2,40,000 = 1,53,600 \]

### Step 4: Calculate the number of educated women
To find the number of educated women, we subtract the number of educated men from the total number of educated people.

\[ \text{Number of educated women} = \text{Total educated people} - \text{Number of educated men} = 1,53,600 - 1,18,800 = 34,800 \]

### Step 5: Calculate the percentage of educated women
Now, we need to find the percentage of educated women out of the total number of women.

\[ \text{Percentage of educated women} = \left( \frac{\text{Number of educated women}}{\text{Total number of women}} \right) \times 100 = \left( \frac{34,800}{1,08,000} \right) \times 100 \]

Calculating this gives:

\[ \text{Percentage of educated women} = \left( \frac{34,800}{1,08,000} \right) \times 100 \approx 32.22\% \]

### Final Answer
The percentage of educated women in the city is approximately **32.22%**.

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