In a colony of 200 members, 85 people read English newspaper, 53 people read Hindi newspaper and 120 read Telugu newspaper, 12 read newspapers of all the three languages, 21 read English and Hindi newspapers, 17 read Hindi and Telugu newspapers.
Find the number of people who read only of the newspapers.

Options

A. 80
B. 94
C. 103
D. 114

Explanation

To solve the problem step-by-step, we will use the principle of inclusion-exclusion and a Venn diagram to find the number of people who read only one type of newspaper.

### Step 1: Define the sets
Let:
- \( E \) = number of people who read the English newspaper = 85
- \( H \) = number of people who read the Hindi newspaper = 53
- \( T \) = number of people who read the Telugu newspaper = 120
- \( E \cap H \cap T \) = number of people who read all three newspapers = 12
- \( E \cap H \) = number of people who read both English and Hindi = 21
- \( H \cap T \) = number of people who read both Hindi and Telugu = 17
- \( T \cap E \) = number of people who read both Telugu and English = 52

### Step 2: Set up the Venn Diagram
We will denote:
- \( x \) = number of people who read only English
- \( y \) = number of people who read only Hindi
- \( z \) = number of people who read only Telugu
- \( a \) = number of people who read English and Hindi but not Telugu
- \( b \) = number of people who read Hindi and Telugu but not English
- \( c \) = number of people who read Telugu and English but not Hindi
- \( g \) = number of people who read all three newspapers = 12

### Step 3: Write equations based on the information given
From the information provided, we can write the following equations:
1. \( a + g = E \cap H \) → \( a + 12 = 21 \) → \( a = 9 \)
2. \( b + g = H \cap T \) → \( b + 12 = 17 \) → \( b = 5 \)
3. \( c + g = T \cap E \) → \( c + 12 = 52 \) → \( c = 40 \)

### Step 4: Calculate the number of people who read only one newspaper
Using the total counts:
- For English:
\[ x + a + c + g = E \implies x + 9 + 40 + 12 = 85 \implies x + 61 = 85 \implies x = 24 \]
- For Hindi:
\[ y + a + b + g = H \implies y + 9 + 5 + 12 = 53 \implies y + 26 = 53 \implies y = 27 \]
- For Telugu:
\[ z + b + c + g = T \implies z + 5 + 40 + 12 = 120 \implies z + 57 = 120 \implies z = 63 \]

### Step 5: Calculate the total number of people who read only one newspaper
Now, we can find the total number of people who read only one type of newspaper:
\[ \text{Total} = x + y + z = 24 + 27 + 63 = 114 \]

### Final Answer
The number of people who read only one type of newspaper is **114**.

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