In an examination 75% candidates passed in English and 60% passed in Mathematics. 25% failed in both and 240 passed the examination. Find the total number of candidates.

Options

A. 492
B. 300
C. 500
D. 400

Answer

To solve the problem step by step, we will use the information provided in the question.

### Step 1: Define the Variables
Let the total number of candidates be \( N \).

### Step 2: Calculate the Percentage of Candidates Who Passed and Failed
- Candidates who passed in English = 75% of \( N \)
- Candidates who passed in Mathematics = 60% of \( N \)
- Candidates who failed in both subjects = 25% of \( N \)

### Step 3: Calculate the Candidates Who Passed in At Least One Subject
If 25% failed in both, then the percentage of candidates who passed in at least one subject is:
\[ 100\% - 25\% = 75\% \]
Thus, the number of candidates who passed in at least one subject is:
\[ 0.75N \]

### Step 4: Set Up the Equation
We know that the number of candidates who passed the examination is given as 240. Therefore, we can set up the equation:
\[ 0.75N = 240 \]

### Step 5: Solve for \( N \)
To find \( N \), we rearrange the equation:
\[ N = \frac{240}{0.75} \]
Calculating this gives:
\[ N = \frac{240 \times 100}{75} = \frac{24000}{75} = 320 \]

### Step 6: Final Calculation
Now, to simplify \( \frac{24000}{75} \):
- Divide both the numerator and denominator by 15:
\[ \frac{24000 \div 15}{75 \div 15} = \frac{1600}{5} = 320 \]

### Conclusion
Thus, the total number of candidates is:
\[ N = 320 \]