The table given below shows the percent-age of literate people in 6 cities . This table also shows the ratio of males to females among literate people .
`{:("City","%of literate people ","Males : Females"),(" " 1," "80," "4:5),(" "2," "85," "7 :4),(" "3," "78," "3 : 2),(" "4," "63," "1 : 1),(" "5," "92," "9 : 7 ),(" "6 ," "58," "2 : 3):}`
% of literate people of any city = (Literate people of the city / Total population of the city ) `xx 100`
If there are 259210 literate females in city 5, what is the total population of city 5 ?

Options

A. 644000
B. 354200
C. 690000
D. 483000

Answer

To find the total population of city 5 given the number of literate females, we can follow these steps:

### Step 1: Understand the given data
From the table, we know:
- Percentage of literate people in city 5 = 92%
- Ratio of males to females among literate people = 9:7
- Number of literate females in city 5 = 259,210

### Step 2: Calculate the number of literate males
Let the number of literate males be \( x \). According to the ratio of males to females (9:7), we can express this as:
\[ \frac{x}{259210} = \frac{9}{7} \]

### Step 3: Cross-multiply to find \( x \)
Cross-multiplying gives us:
\[ 7x = 9 \times 259210 \]
Now, calculate \( 9 \times 259210 \):
\[ 9 \times 259210 = 2332890 \]
So, we have:
\[ 7x = 2332890 \]
Now, divide both sides by 7 to find \( x \):
\[ x = \frac{2332890}{7} = 333270 \]

### Step 4: Calculate the total number of literate people
Now, we can find the total number of literate people in city 5 by adding the number of literate males and females:
\[ \text{Total literate people} = \text{Literate males} + \text{Literate females} = 333270 + 259210 = 592480 \]

### Step 5: Use the percentage to find the total population
We know that the percentage of literate people is given by:
\[ \text{Percentage of literate people} = \left(\frac{\text{Literate population}}{\text{Total population}}\right) \times 100 \]
Substituting the known values:
\[ 92 = \left(\frac{592480}{\text{Total population}}\right) \times 100 \]

### Step 6: Rearrange to find the total population
Rearranging the equation gives:
\[ \text{Total population} = \frac{592480 \times 100}{92} \]
Calculating this:
\[ \text{Total population} = \frac{59248000}{92} = 644000 \]

### Conclusion
The total population of city 5 is **644,000**.

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