In an examination `70%` of the total examinee passed. If the number of failures is 420, the total number of examinees is

Options

A. 1400
B. 1200
C. 1000
D. 693

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the total number of examinees
Let the total number of examinees be represented by \( x \).

### Step 2: Determine the percentage of failures
Since 70% of the examinees passed, the percentage of failures is:
\[ 100\% - 70\% = 30\% \]
This means that 30% of the total examinees failed.

### Step 3: Set up the equation for failures
According to the problem, the number of failures is given as 420. Therefore, we can write:
\[ 30\% \text{ of } x = 420 \]
This can be expressed mathematically as:
\[ \frac{30}{100} \cdot x = 420 \]

### Step 4: Simplify the equation
To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ 30x = 420 \cdot 100 \]
\[ 30x = 42000 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 30 to find \( x \):
\[ x = \frac{42000}{30} \]
Calculating the right side:
\[ x = 1400 \]

### Conclusion
The total number of examinees is \( 1400 \).