While preparing the progress reports of the students the class teacher found that 70% of the students passed in Hindi , 80 % passed English and only 65% passed in both the subject . Find out the percentage of students who failed in both the subject.

Options

A. 0.15
B. 0.2
C. 0.3
D. 0.35

Explanation

To solve the problem step by step, we will use the information provided about the percentages of students passing in Hindi and English, as well as those passing in both subjects.

### Step 1: Identify the given data
- Percentage of students who passed in Hindi (H) = 70%
- Percentage of students who passed in English (E) = 80%
- Percentage of students who passed in both subjects (H ∩ E) = 65%

### Step 2: Use the formula for the union of two sets
The formula for the union of two sets is given by:
\[ H \cup E = H + E - (H \cap E) \]
Where:
- \( H \cup E \) is the percentage of students who passed in at least one subject (either Hindi or English).
- \( H \) is the percentage of students who passed in Hindi.
- \( E \) is the percentage of students who passed in English.
- \( H \cap E \) is the percentage of students who passed in both subjects.

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ H \cup E = 70\% + 80\% - 65\% \]

### Step 4: Calculate the union
Now, perform the calculation:
\[ H \cup E = 70 + 80 - 65 = 85\% \]
This means that 85% of the students passed in at least one of the subjects (Hindi or English).

### Step 5: Calculate the percentage of students who failed in both subjects
To find the percentage of students who failed in both subjects, we subtract the percentage of students who passed in at least one subject from 100%:
\[ \text{Percentage of students who failed in both} = 100\% - H \cup E \]
Substituting the value we calculated:
\[ \text{Percentage of students who failed in both} = 100\% - 85\% = 15\% \]

### Final Answer
Thus, the percentage of students who failed in both subjects is **15%**.

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