In a class 60% of the student pass in Hindi and 45 % pass in Sanskrit. If 25% of them pass in both subject, what percentage of the students fail in both the subjects ?

Options

A. 0.8
B. 0.75
C. 0.2
D. 0.25

Answer

To solve the problem, we will use the principle of inclusion-exclusion to find the percentage of students who fail in both subjects.

### Step-by-step Solution:

1. **Identify the given percentages:**
- Let \( P(H) \) be the percentage of students who pass in Hindi = 60%
- Let \( P(S) \) be the percentage of students who pass in Sanskrit = 45%
- Let \( P(H \cap S) \) be the percentage of students who pass in both subjects = 25%

2. **Use the principle of inclusion-exclusion:**
The formula to find the percentage of students who pass in at least one subject is:
\[ P(H \cup S) = P(H) + P(S) - P(H \cap S) \]

3. **Substitute the values into the formula:**
\[ P(H \cup S) = 60\% + 45\% - 25\% \]
\[ P(H \cup S) = 105\% - 25\% = 80\% \]

4. **Calculate the percentage of students who fail in both subjects:**
The percentage of students who fail in both subjects is given by:
\[ P(\text{Fail in both}) = 100\% - P(H \cup S) \]
\[ P(\text{Fail in both}) = 100\% - 80\% = 20\% \]

5. **Conclusion:**
Therefore, the percentage of students who fail in both subjects is **20%**.