In a city , `32%` of the population is composed of migrants . `25%` of whom are from rural areas. `41(3)/(17)%` is female of the local population while this figure for rural and urban migrants is `75%` and `25%` females respectively. If the total population of the city is `728400` what is its female populations ?

Options

A. `460000`
B. `238500`
C. `600000`
D. `291360`

Answer

To find the female population in the city, we will follow these steps:

### Step 1: Calculate the total number of migrants.
The total population of the city is given as 728,400, and 32% of this population is composed of migrants.

\[ \text{Migrants} = 32\% \text{ of } 728400 = \frac{32}{100} \times 728400 = 233088 \]

### Step 2: Calculate the number of rural migrants.
25% of the migrants are from rural areas.

\[ \text{Rural Migrants} = 25\% \text{ of } 233088 = \frac{25}{100} \times 233088 = 58272 \]

### Step 3: Calculate the local population.
The local population is the total population minus the number of migrants.

\[ \text{Local Population} = 728400 - 233088 = 495312 \]

### Step 4: Calculate the number of females in the local population.
41 \( \frac{3}{17} \% \) of the local population is female. First, convert \( 41 \frac{3}{17} \) to an improper fraction.

\[ 41 \frac{3}{17} = \frac{41 \times 17 + 3}{17} = \frac{697 + 3}{17} = \frac{700}{17} \]

Now calculate the number of females in the local population:

\[ \text{Females in Local Population} = \frac{700}{17} \% \text{ of } 495312 = \frac{700}{17} \times \frac{1}{100} \times 495312 = \frac{700 \times 495312}{1700} = 203952 \]

### Step 5: Calculate the number of urban migrants.
Urban migrants are the total migrants minus the rural migrants.

\[ \text{Urban Migrants} = 233088 - 58272 = 174816 \]

### Step 6: Calculate the number of females among rural migrants.
75% of rural migrants are female.

\[ \text{Females in Rural Migrants} = 75\% \text{ of } 58272 = \frac{75}{100} \times 58272 = 43704 \]

### Step 7: Calculate the number of females among urban migrants.
25% of urban migrants are female.

\[ \text{Females in Urban Migrants} = 25\% \text{ of } 174816 = \frac{25}{100} \times 174816 = 43704 \]

### Step 8: Calculate the total female population.
Now, add the number of females from the local population, rural migrants, and urban migrants.

\[ \text{Total Female Population} = \text{Females in Local Population} + \text{Females in Rural Migrants} + \text{Females in Urban Migrants} \]

\[ \text{Total Female Population} = 203952 + 43704 + 43704 = 291360 \]

### Final Answer:
The total female population in the city is **291360**.

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