In an examination `65%` of the total examinees passed. If the number of failures is `420,` the total number of examinees is

Options

A. `500`
B. `100`
C. `1200`
D. `1625`

Answer

To find the total number of examinees based on the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that 65% of the total examinees passed the examination, and the number of failures is given as 420.

2. **Define Variables**: Let the total number of examinees be represented by \( x \).

3. **Calculate the Percentage of Failures**: Since 65% passed, the percentage of failures is:
\[ 100\% - 65\% = 35\% \]

4. **Set Up the Equation**: We know that 35% of the total examinees equals the number of failures (420). Therefore, we can write the equation:
\[ 35\% \text{ of } x = 420 \]
This can be expressed mathematically as:
\[ \frac{35}{100} \times x = 420 \]

5. **Solve for \( x \)**: To isolate \( x \), we can multiply both sides of the equation by \( \frac{100}{35} \):
\[ x = 420 \times \frac{100}{35} \]

6. **Calculate the Right Side**: First, simplify \( \frac{100}{35} \):
\[ \frac{100}{35} = \frac{20}{7} \]
Now, substitute this back into the equation:
\[ x = 420 \times \frac{20}{7} \]

7. **Perform the Multiplication**:
\[ x = 420 \div 7 \times 20 \]
Calculate \( 420 \div 7 = 60 \):
\[ x = 60 \times 20 = 1200 \]

8. **Conclusion**: The total number of examinees is:
\[ \boxed{1200} \]