In a class `70% ` of students pass in English Exam and ` 65%` students pass in Maths exam and `27% `of students fail in Both subjects and 248 students pass in both subjects. Find the total number of students.

Answer

To solve the problem step by step, we will use the information provided in the question and apply the principles of percentages.

### Step 1: Understand the given percentages
We know:
- 70% of students pass in English.
- 65% of students pass in Maths.
- 27% of students fail in both subjects.
- 248 students pass in both subjects.

### Step 2: Calculate the percentage of students who pass in at least one subject
Since 27% of students fail in both subjects, the percentage of students who pass in at least one subject is:
\[ 100\% - 27\% = 73\% \]

### Step 3: Set up the equation for passing students
Let \( x \) be the total number of students. The number of students passing in English, Maths, and both can be represented as follows:
- Students passing in English: \( 0.70x \)
- Students passing in Maths: \( 0.65x \)
- Students passing in both subjects: \( 248 \)

Using the principle of inclusion-exclusion for the total number of students passing in at least one subject:
\[ \text{Pass in at least one subject} = \text{Pass in English} + \text{Pass in Maths} - \text{Pass in both} \]
This gives us:
\[ 0.73x = 0.70x + 0.65x - 248 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 0.73x = 1.35x - 248 \]
Now, rearranging the equation to isolate \( x \):
\[ 248 = 1.35x - 0.73x \]
\[ 248 = 0.62x \]

### Step 5: Solve for \( x \)
Now, divide both sides by 0.62 to find the total number of students:
\[ x = \frac{248}{0.62} \]
Calculating this gives:
\[ x = 400 \]

### Conclusion
The total number of students in the class is **400**.

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