The average marks obtained by 240 students in a certain examination is 35. If the average marks of the passed candidates are 39 and that of the failed candidates are 15, then the total number of candidates who passed the examination is:

Options

A. 225
B. 180
C. 200
D. 210

Answer

To solve the problem, we will use the concept of averages and the total marks obtained by the students.

### Step-by-Step Solution:

1. **Calculate the Total Marks of All Students:**
The average marks of all 240 students is 35. Therefore, the total marks obtained by all students can be calculated as:
\[ \text{Total Marks} = \text{Average Marks} \times \text{Number of Students} = 35 \times 240 = 8400 \]

2. **Let the Number of Passed Candidates be \( x \):**
If \( x \) students passed the examination, then the number of failed candidates will be \( 240 - x \).

3. **Calculate the Total Marks of Passed and Failed Candidates:**
The average marks of the passed candidates is 39, so the total marks of the passed candidates is:
\[ \text{Total Marks of Passed Candidates} = 39x \]
The average marks of the failed candidates is 15, so the total marks of the failed candidates is:
\[ \text{Total Marks of Failed Candidates} = 15(240 - x) \]

4. **Set Up the Equation:**
The total marks obtained by all students is the sum of the total marks of passed and failed candidates:
\[ 39x + 15(240 - x) = 8400 \]

5. **Simplify the Equation:**
Expanding the equation:
\[ 39x + 3600 - 15x = 8400 \]
Combine like terms:
\[ 24x + 3600 = 8400 \]

6. **Isolate \( x \):**
Subtract 3600 from both sides:
\[ 24x = 8400 - 3600 \]
\[ 24x = 4800 \]
Now, divide both sides by 24:
\[ x = \frac{4800}{24} = 200 \]

7. **Conclusion:**
Therefore, the total number of candidates who passed the examination is \( \boxed{200} \).