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`
Total population of city 6 is 200000 and the total population of city 2 is 220000 . What is the respective ratio of literate males of city 2 and literate females of city 6 ?

Options

A. 348 : 595
B. 255 : 199
C. 595 : 348
D. 199 : 255

Answer

To solve the problem, we need to find the ratio of literate males in City 2 to literate females in City 6. We will follow these steps:

### Step 1: Calculate the number of literate people in City 6
- Given that the total population of City 6 is 200,000 and the percentage of literate people is 58%.
- We can use the formula:

\[ \text{Literate People} = \left(\frac{\text{Percentage of Literate People}}{100}\right) \times \text{Total Population} \]

Substituting the values:

\[ \text{Literate People in City 6} = \left(\frac{58}{100}\right) \times 200000 = 116000 \]

### Step 2: Determine the number of literate males and females in City 6
- The ratio of males to females in City 6 is given as 2:3.
- Let the number of literate males be \(2x\) and the number of literate females be \(3x\).
- The total literate people in City 6 is:

\[ 2x + 3x = 5x = 116000 \]

- Solving for \(x\):

\[ x = \frac{116000}{5} = 23200 \]

- Therefore, the number of literate females in City 6 is:

\[ \text{Literate Females in City 6} = 3x = 3 \times 23200 = 69600 \]

### Step 3: Calculate the number of literate people in City 2
- Given that the total population of City 2 is 220,000 and the percentage of literate people is 85%.
- Using the same formula:

\[ \text{Literate People in City 2} = \left(\frac{85}{100}\right) \times 220000 = 187000 \]

### Step 4: Determine the number of literate males and females in City 2
- The ratio of males to females in City 2 is given as 7:4.
- Let the number of literate males be \(7y\) and the number of literate females be \(4y\).
- The total literate people in City 2 is:

\[ 7y + 4y = 11y = 187000 \]

- Solving for \(y\):

\[ y = \frac{187000}{11} = 17000 \]

- Therefore, the number of literate males in City 2 is:

\[ \text{Literate Males in City 2} = 7y = 7 \times 17000 = 119000 \]

### Step 5: Find the ratio of literate males in City 2 to literate females in City 6
- We have:
- Literate Males in City 2 = 119000
- Literate Females in City 6 = 69600

- The ratio is:

\[ \text{Ratio} = \frac{\text{Literate Males in City 2}}{\text{Literate Females in City 6}} = \frac{119000}{69600} \]

### Step 6: Simplifying the ratio
- To simplify, we can divide both numbers by 100:

\[ \frac{1190}{696} \]

- Now we can simplify further by finding the greatest common divisor (GCD). Dividing both by 2:

\[ \frac{595}{348} \]

### Final Answer
The ratio of literate males in City 2 to literate females in City 6 is \(595:348\).

---