In an examination 65% students pass in History and 55% students pass in Hindi. If 5% students fail in both the subjects, then what is the percentage of students who have passed in both the subjects?

Options

A. 15
B. 20
C. 25
D. 30

Answer

To solve the problem, we need to determine the percentage of students who passed in both History and Hindi. Let's break it down step by step.

### Step 1: Understand the given data
- Percentage of students passing in History = 65%
- Percentage of students passing in Hindi = 55%
- Percentage of students failing in both subjects = 5%

### Step 2: Calculate the percentage of students passing in at least one subject
Since 5% of students fail in both subjects, it means that 95% of students pass in at least one subject (either History or Hindi or both).

### Step 3: Set up the equation
Let \( x \) be the percentage of students who passed in both subjects. According to the principle of inclusion-exclusion for sets, we can express the total percentage of students passing in at least one subject as follows:

\[ \text{Percentage passing in at least one subject} = \text{Percentage passing in History} + \text{Percentage passing in Hindi} - \text{Percentage passing in both subjects} \]

Substituting the known values into the equation gives us:

\[ 95 = 65 + 55 - x \]

### Step 4: Simplify the equation
Now, simplify the equation:

\[ 95 = 120 - x \]

### Step 5: Solve for \( x \)
Rearranging the equation to solve for \( x \):

\[ x = 120 - 95 \]
\[ x = 25 \]

### Conclusion
Thus, the percentage of students who passed in both subjects is **25%**.

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