In a class, 300 students speak Hindi, 150 students speak English and 100 students speak both Hindi and English. Then, total number of students is

Options

A. 100
B. 120
C. 160
D. 350

Answer

To find the total number of students in the class who speak either Hindi or English or both, we can use the principle of inclusion-exclusion. Here’s a step-by-step solution:

### Step 1: Define the Sets
Let:
- \( A \) be the set of students who speak Hindi.
- \( B \) be the set of students who speak English.

From the problem, we know:
- \( |A| = 300 \) (the number of students who speak Hindi)
- \( |B| = 150 \) (the number of students who speak English)
- \( |A \cap B| = 100 \) (the number of students who speak both Hindi and English)

### Step 2: Use the Inclusion-Exclusion Principle
The formula for the total number of students who speak either Hindi or English (or both) is given by:
\[ |A \cup B| = |A| + |B| - |A \cap B| \]

### Step 3: Substitute the Values
Now, we can substitute the values we have into the formula:
\[ |A \cup B| = 300 + 150 - 100 \]

### Step 4: Calculate the Total
Now, perform the arithmetic:
\[ |A \cup B| = 300 + 150 - 100 = 350 \]

### Conclusion
Thus, the total number of students in the class is \( 350 \).

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