In a city `45%` of the people read English and Hindi newspapers. `15%` read only Urdu newspaper and `75%` read Hindi newspaper. If nobody reads all the three newspapers and everybody read atleast one newspaper out of English, Hindi and Urdu newspapers, how many read Urdu newspaper?

Options

A. Max `45%`
B. Max. `55%`
C. Min `25%`
D. Min `30%`

Answer

To solve the problem step by step, we need to analyze the information given and use set theory concepts.

### Step 1: Define the Variables
Let:
- \( E \) = Percentage of people reading English newspapers
- \( H \) = Percentage of people reading Hindi newspapers
- \( U \) = Percentage of people reading Urdu newspapers
- \( EH \) = Percentage of people reading both English and Hindi newspapers
- \( EU \) = Percentage of people reading both English and Urdu newspapers
- \( HU \) = Percentage of people reading both Hindi and Urdu newspapers
- \( EHU \) = Percentage of people reading all three newspapers (which is given as 0%)

### Step 2: Write the Given Information
From the problem, we have:
- \( EH = 45\% \) (people reading both English and Hindi)
- \( U \) (only reading Urdu) = \( 15\% \)
- \( H = 75\% \) (people reading Hindi)
- \( EHU = 0\% \) (no one reads all three newspapers)

### Step 3: Use the Total Percentage Equation
According to set theory, the total percentage of people reading at least one newspaper can be expressed as:
\[ E + H + U - EH - EU - HU + EHU = 100\% \]
Since \( EHU = 0\% \), the equation simplifies to:
\[ E + H + U - EH - EU - HU = 100\% \]

### Step 4: Substitute Known Values
Substituting the known values into the equation:
\[ E + 75 + U - 45 - EU - HU = 100 \]
This simplifies to:
\[ E + U - EU - HU = 70 \]

### Step 5: Determine the Values of \( E \), \( EU \), and \( HU \)
We know that:
- \( E + H = EH + EU + HU + EHU \)
- Since \( EHU = 0\), we can express \( U \) in terms of \( EU \) and \( HU \).

Using the information:
1. From \( H = 75\% \) and \( EH = 45\% \), we can find \( HU \):
\[ HU = H - EH = 75 - 45 = 30\% \]

2. Now substitute \( HU \) back into the equation:
\[ E + U - EU - 30 = 70 \]
Rearranging gives:
\[ E + U - EU = 100 \]

### Step 6: Calculate the Percentage of People Reading Urdu Newspapers
From the previous steps, we know:
- \( U = 15\% \) (only reading Urdu)
- We need to find the total percentage of people reading Urdu, which includes those reading Urdu with either English or Hindi.

Using the equation:
\[ U = 15 + EU + HU \]
Substituting \( HU = 30\):
\[ U = 15 + EU + 30 \]
Thus,
\[ U = 45 + EU \]

### Step 7: Solve for \( U \)
Since \( U \) must be a percentage that does not exceed 100%, we can conclude:
\[ U = 15 + EU + 30 \]
Thus, the total percentage of people reading Urdu newspapers is:
\[ U = 15 + 0 + 30 = 45\% \]

### Final Answer
The total percentage of people reading Urdu newspapers is \( 45\% \).