In an examination, 52% students failed in Hindi and 42% failed in English. If 17% failed in both the subjects, what percentage of students passed in both the subjects ?

Options

A. 38%
B. 33%
C. 23%
D. 18%

Answer

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

### Step 1: Identify the given percentages
- Percentage of students who failed in Hindi (H) = 52%
- Percentage of students who failed in English (E) = 42%
- Percentage of students who failed in both subjects (H ∩ E) = 17%

### Step 2: Use the principle of inclusion-exclusion to find the total percentage of students who failed in at least one subject
The formula for the percentage of students who failed in at least one subject is:
\[ P(H \cup E) = P(H) + P(E) - P(H \cap E) \]
Substituting the given values:
\[ P(H \cup E) = 52\% + 42\% - 17\% \]

### Step 3: Calculate the total percentage of students who failed in at least one subject
\[ P(H \cup E) = 52 + 42 - 17 = 77\% \]
This means that 77% of students failed in at least one subject.

### Step 4: Calculate the percentage of students who passed in both subjects
To find the percentage of students who passed in both subjects, we subtract the percentage of students who failed in at least one subject from 100%:
\[ P(\text{Passed in both}) = 100\% - P(H \cup E) \]
Substituting the value we calculated:
\[ P(\text{Passed in both}) = 100\% - 77\% = 23\% \]

### Conclusion
The percentage of students who passed in both subjects is **23%**.

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