If 30% students failed in History, 45% failed in Politics and 25% failed in both the subjects then how many students passed in both the subjects?

Options

A. `60%`
B. `45%`
C. `50%`
D. `40%`

Answer

To solve the problem, we need to determine how many students passed in both History and Politics given the percentages of students who failed in each subject and those who failed in both.

### Step-by-step Solution:

1. **Identify the percentages of students failing in each subject:**
- Let \( F_H \) be the percentage of students who failed in History.
- Let \( F_P \) be the percentage of students who failed in Politics.
- Let \( F_{HP} \) be the percentage of students who failed in both subjects.

From the question:
- \( F_H = 30\% \)
- \( F_P = 45\% \)
- \( F_{HP} = 25\% \)

2. **Calculate the total percentage of students who failed in at least one subject:**
- We can use the principle of inclusion-exclusion to find the total percentage of students who failed in at least one subject:
\[ F_{H \cup P} = F_H + F_P - F_{HP} \]
Substituting the values:
\[ F_{H \cup P} = 30\% + 45\% - 25\% = 50\% \]

3. **Determine the percentage of students who passed in both subjects:**
- The percentage of students who passed in both subjects is the complement of those who failed in at least one subject:
\[ P_{both} = 100\% - F_{H \cup P} \]
Substituting the value we found:
\[ P_{both} = 100\% - 50\% = 50\% \]

### Final Answer:
Thus, the percentage of students who passed in both subjects is **50%**.