In an examination 55% students passed in English, 35% students passed in Mathematics and 20% tudents passed in both the subjects. If 1200 students are failed then how many students appeared in the examination?

Options

A. 4800
B. 4000
C. 3600
D. 3200

Answer

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

### Step 1: Understand the given percentages
- Let \( P \) be the total number of students who appeared for the examination.
- 55% of students passed in English.
- 35% of students passed in Mathematics.
- 20% of students passed in both subjects.

### Step 2: Calculate the percentage of students who failed
- The percentage of students who failed in English = \( 100\% - 55\% = 45\% \)
- The percentage of students who failed in Mathematics = \( 100\% - 35\% = 65\% \)
- The percentage of students who passed in both subjects = 20%, so the percentage of students who failed in both subjects is \( 100\% - 20\% = 80\% \)

### Step 3: Use the principle of inclusion-exclusion
To find the total percentage of students who failed in at least one subject, we can use the formula:
\[ \text{Failed in at least one subject} = \text{Failed in English} + \text{Failed in Mathematics} - \text{Failed in both} \]
Substituting the values we calculated:
\[ \text{Failed in at least one subject} = 45\% + 65\% - 80\% = 30\% \]

### Step 4: Relate the percentage of students who failed to the total number of students
We know that 1200 students failed, which corresponds to 30% of the total students \( P \):
\[ 30\% \text{ of } P = 1200 \]
This can be written mathematically as:
\[ \frac{30}{100} \times P = 1200 \]

### Step 5: Solve for \( P \)
To find \( P \), we rearrange the equation:
\[ P = \frac{1200 \times 100}{30} \]
Calculating this gives:
\[ P = \frac{120000}{30} = 4000 \]

### Conclusion
The total number of students who appeared for the examination is \( 4000 \).