In an examination `48%` of the students failed in Hindi `32%` of the student failed in history, `20%` of the students failed in both subjects. If the number of students who passed the examination 880 in both subjects . Find the total students ?

Options

A. `2100`
B. `2000`
C. `2200`
D. `2600`

Answer

To solve the problem, we will use the principle of inclusion-exclusion to find the total number of students.

### Step-by-Step Solution:

1. **Define Variables**:
Let the total number of students be \( x \).

2. **Calculate the Percentage of Students Who Failed**:
- Students who failed in Hindi = \( 48\% \) of \( x \) = \( 0.48x \)
- Students who failed in History = \( 32\% \) of \( x \) = \( 0.32x \)
- Students who failed in both subjects = \( 20\% \) of \( x \) = \( 0.20x \)

3. **Use the Inclusion-Exclusion Principle**:
The number of students who failed in at least one subject can be calculated as:
\[ \text{Failed in Hindi} + \text{Failed in History} - \text{Failed in both} \]
Thus, the total number of students who failed in at least one subject is:
\[ 0.48x + 0.32x - 0.20x = 0.60x \]

4. **Calculate the Percentage of Students Who Passed**:
The percentage of students who passed in both subjects is:
\[ 100\% - 60\% = 40\% \]
Therefore, the number of students who passed is:
\[ 0.40x \]

5. **Set Up the Equation**:
We know that the number of students who passed is given as 880:
\[ 0.40x = 880 \]

6. **Solve for \( x \)**:
To find \( x \), divide both sides by \( 0.40 \):
\[ x = \frac{880}{0.40} = 2200 \]

7. **Conclusion**:
The total number of students is \( 2200 \).

### Final Answer:
The total number of students is **2200**.

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