In a group of 20 people, 8 read Hindi, 11 read English while 5 of them read none of these two. How many of them read Hindi and English both ?

Options

A. 8
B. 6
C. 4
D. 2

Explanation

To solve the problem step by step, we can use the principle of inclusion-exclusion. Here’s how we can approach it:

### Step-by-Step Solution

1. **Identify the total number of people**:
We know that there are 20 people in total.

2. **Identify the number of people reading each language**:
- Number of people reading Hindi (H) = 8
- Number of people reading English (E) = 11

3. **Identify the number of people reading none**:
- Number of people reading neither Hindi nor English = 5

4. **Calculate the number of people reading at least one language**:
Since 5 people read none of the languages, the number of people reading at least one language is:
\[ \text{People reading at least one language} = \text{Total people} - \text{People reading none} = 20 - 5 = 15 \]

5. **Set up the equation using inclusion-exclusion**:
Let \( x \) be the number of people who read both Hindi and English. According to the principle of inclusion-exclusion, we have:
\[ H + E - x = \text{People reading at least one language} \]
Substituting the known values:
\[ 8 + 11 - x = 15 \]

6. **Solve for \( x \)**:
Rearranging the equation:
\[ 19 - x = 15 \]
\[ x = 19 - 15 \]
\[ x = 4 \]

7. **Conclusion**:
Therefore, the number of people who read both Hindi and English is \( x = 4 \).

### Final Answer:
**4 people read both Hindi and English.**