In an examination, 30% and 35% students failed in physics and chemistry respectively while 27% students failed in both the subjects. If the number of students passing the examination is 248, find the total number of students who appeared in the examination.

Options

A. a. 500
B. b. 400
C. c. 450
D. d. none of these

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Problem
We know that:
- 30% of students failed in Physics.
- 35% of students failed in Chemistry.
- 27% of students failed in both subjects.
- The number of students who passed is 248.

### Step 2: Calculate Total Percentage of Students Who Failed
To find the total percentage of students who failed in at least one subject, we can use the principle of inclusion-exclusion:
- Let \( P \) be the percentage of students who failed in Physics.
- Let \( C \) be the percentage of students who failed in Chemistry.
- Let \( B \) be the percentage of students who failed in both subjects.

Using the formula:
\[ \text{Total failed} = P + C - B \]
Substituting the values:
\[ \text{Total failed} = 30\% + 35\% - 27\% = 38\% \]

### Step 3: Calculate the Percentage of Students Who Passed
The percentage of students who passed the examination can be calculated as:
\[ \text{Percentage passed} = 100\% - \text{Total failed} \]
Substituting the value we found:
\[ \text{Percentage passed} = 100\% - 38\% = 62\% \]

### Step 4: Set Up the Equation
We know that 62% of the total number of students equals 248 (the number of students who passed):
\[ 62\% \text{ of Total Students} = 248 \]
Let \( x \) be the total number of students. We can write the equation as:
\[ 0.62x = 248 \]

### Step 5: Solve for Total Students
To find \( x \), we divide both sides by 0.62:
\[ x = \frac{248}{0.62} \]
Calculating this gives:
\[ x = 400 \]

### Step 6: Conclusion
The total number of students who appeared in the examination is **400**.

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