In a flight 55 people speak Hindi, 20 speak English and 15 speak both English and Hindi. The number of people who speak at least one of the two languages is

Options

A. 40
B. 50
C. 20
D. 60

Answer

To find the number of people who speak at least one of the two languages (Hindi or English), we can use the principle of inclusion-exclusion.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Let \( n(H) \) be the number of people who speak Hindi = 55
- Let \( n(E) \) be the number of people who speak English = 20
- Let \( n(H \cap E) \) be the number of people who speak both Hindi and English = 15

2. **Use the Inclusion-Exclusion Principle**:
The formula to find the number of people who speak at least one of the two languages is given by:
\[ n(H \cup E) = n(H) + n(E) - n(H \cap E) \]
where \( n(H \cup E) \) is the number of people who speak either Hindi or English or both.

3. **Substitute the Values into the Formula**:
\[ n(H \cup E) = 55 + 20 - 15 \]

4. **Calculate the Result**:
- First, add \( n(H) \) and \( n(E) \):
\[ 55 + 20 = 75 \]
- Then subtract \( n(H \cap E) \):
\[ 75 - 15 = 60 \]

5. **Conclusion**:
The number of people who speak at least one of the two languages (Hindi or English) is **60**.