In a town of 1000 people 570 read Hindi newspaper, 424 read English newspaper and 254 read Punjabi newspaper. 40 read only Hindi and Punjabi newspaper , 58 read only Hindi and English newspaper , and 70 read only Punjabi and English newspaper 100 read no newspaper .
How many people read only one newspaper ? How many people read only one newspaper ?

Options

A. 570
B. 642
C. 914
D. 968

Answer

To solve the problem step by step, we will use the given data to find out how many people read only one newspaper.

### Step 1: Define Variables
Let:
- \( H \) = Number of people who read Hindi newspaper = 570
- \( E \) = Number of people who read English newspaper = 424
- \( P \) = Number of people who read Punjabi newspaper = 254
- \( x \) = Number of people who read all three newspapers
- \( n \) = Total number of people = 1000
- \( N \) = Number of people who read no newspaper = 100

### Step 2: Use Given Information
From the problem, we know:
- Number of people who read only Hindi and Punjabi = 40
- Number of people who read only Hindi and English = 58
- Number of people who read only Punjabi and English = 70

### Step 3: Set Up Equations
We can express the number of people who read only one newspaper as follows:
1. Only Hindi readers:
\[ \text{Only Hindi} = H - ( \text{Hindi and Punjabi} + \text{Hindi and English} + x ) = 570 - (40 + 58 + x) = 472 - x \]

2. Only English readers:
\[ \text{Only English} = E - ( \text{Hindi and English} + \text{Punjabi and English} + x ) = 424 - (58 + 70 + x) = 296 - x \]

3. Only Punjabi readers:
\[ \text{Only Punjabi} = P - ( \text{Hindi and Punjabi} + \text{Punjabi and English} + x ) = 254 - (40 + 70 + x) = 144 - x \]

### Step 4: Total People Equation
Now, we can set up the total number of people equation:
\[ \text{Only Hindi} + \text{Only English} + \text{Only Punjabi} + \text{Hindi and Punjabi} + \text{Hindi and English} + \text{Punjabi and English} + x + N = n \]
Substituting the known values:
\[ (472 - x) + (296 - x) + (144 - x) + 40 + 58 + 70 + x + 100 = 1000 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ (472 + 296 + 144 + 40 + 58 + 70 + 100) - 2x = 1000 \]
Calculating the sum:
\[ 1080 - 2x = 1000 \]

### Step 6: Solve for \( x \)
Rearranging gives:
\[ -2x = 1000 - 1080 \]
\[ -2x = -80 \]
\[ x = 40 \]

### Step 7: Calculate Only One Newspaper Readers
Now substitute \( x \) back into the equations for only one newspaper:
1. Only Hindi:
\[ 472 - 40 = 432 \]

2. Only English:
\[ 296 - 40 = 256 \]

3. Only Punjabi:
\[ 144 - 40 = 104 \]

### Step 8: Total Only One Newspaper Readers
Now, add the numbers of people who read only one newspaper:
\[ 432 + 256 + 104 = 792 \]

### Final Answer
The total number of people who read only one newspaper is **792**.

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