In a class of 60 students, 25 speaks. Hindi, 45 speak English. How many of them speak both English and Hindi, if each student speaks either English or Hindi?

Answer

To solve the problem, we can use the principle of inclusion-exclusion. Let's denote:

- Let \( A \) be the set of students who speak Hindi.
- Let \( B \) be the set of students who speak English.

From the problem, we have:

- Total number of students \( |A \cup B| = 60 \)
- Number of students who speak Hindi \( |A| = 25 \)
- Number of students who speak English \( |B| = 45 \)

We want to find the number of students who speak both languages, denoted as \( |A \cap B| \).

According to the principle of inclusion-exclusion, we have:

\[ |A \cup B| = |A| + |B| - |A \cap B| \]

Substituting the known values into the equation:

\[ 60 = 25 + 45 - |A \cap B| \]

Now, simplify the equation:

\[ 60 = 70 - |A \cap B| \]

To isolate \( |A \cap B| \), we can rearrange the equation:

\[ |A \cap B| = 70 - 60 \]

Calculating the right side gives:

\[ |A \cap B| = 10 \]

Thus, the number of students who speak both Hindi and English is \( 10 \).

### Final Answer:
10 students speak both languages.

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