In an examination of bank P.O., 40% students failed in Mathematics and 30% failed in English, while 20% failed in Mathematics and English both. What percentage of the students passed in both ?

Options

A. 0.48
B. 0.5
C. 0.7
D. None of these

Answer

To solve the problem, we need to determine the percentage of students who passed in both Mathematics and English. We can use the principle of inclusion-exclusion to find this.

### Step-by-Step Solution:

1. **Identify the Given Percentages**:
- Let \( P(M) \) be the percentage of students who failed in Mathematics: \( P(M) = 40\% \).
- Let \( P(E) \) be the percentage of students who failed in English: \( P(E) = 30\% \).
- Let \( P(M \cap E) \) be the percentage of students who failed in both Mathematics and English: \( P(M \cap E) = 20\% \).

2. **Use the Inclusion-Exclusion Principle**:
The percentage of students who failed in either Mathematics or English (or both) can be calculated as follows:
\[ P(M \cup E) = P(M) + P(E) - P(M \cap E) \]
Substituting the values:
\[ P(M \cup E) = 40\% + 30\% - 20\% = 50\% \]

3. **Calculate the Percentage of Students Who Passed in Both**:
The percentage of students who passed in both subjects is the complement of those who failed in either subject:
\[ P(\text{Passed in both}) = 100\% - P(M \cup E) \]
Substituting the value we found:
\[ P(\text{Passed in both}) = 100\% - 50\% = 50\% \]

### Final Answer:
The percentage of students who passed in both Mathematics and English is **50%**.