In an examination 73% of the candidates passed in quantitative aptitude test, 70% passed in General awareness and 64% passed in both. If 6300 failed in both subjects the total number of examinees was

Options

A. 60000
B. 50000
C. 30000
D. 25000

Answer

To solve the problem step-by-step, we will use the information provided about the percentages of candidates who passed in the quantitative aptitude test, general awareness, and both subjects. We will also use the number of candidates who failed both subjects to find the total number of examinees.

### Step 1: Define the variables
Let the total number of examinees be denoted as \( N \).

### Step 2: Calculate the number of candidates who passed in each subject
- Candidates who passed in quantitative aptitude = \( 73\% \) of \( N \) = \( 0.73N \)
- Candidates who passed in general awareness = \( 70\% \) of \( N \) = \( 0.70N \)
- Candidates who passed in both subjects = \( 64\% \) of \( N \) = \( 0.64N \)

### Step 3: Use the principle of inclusion-exclusion
To find the total number of candidates who passed at least one subject, we can use the formula:
\[ \text{Passed in at least one subject} = (\text{Passed in Quantitative Aptitude}) + (\text{Passed in General Awareness}) - (\text{Passed in both}) \]
Substituting the values we have:
\[ \text{Passed in at least one subject} = 0.73N + 0.70N - 0.64N \]
\[ = (0.73 + 0.70 - 0.64)N \]
\[ = 0.79N \]

### Step 4: Calculate the number of candidates who failed both subjects
The number of candidates who failed both subjects is given as \( 6300 \). Therefore, the number of candidates who passed at least one subject can also be expressed as:
\[ \text{Passed in at least one subject} = N - 6300 \]

### Step 5: Set up the equation
Now we can set the two expressions for the number of candidates who passed at least one subject equal to each other:
\[ 0.79N = N - 6300 \]

### Step 6: Solve for \( N \)
Rearranging the equation:
\[ N - 0.79N = 6300 \]
\[ 0.21N = 6300 \]
\[ N = \frac{6300}{0.21} \]
\[ N = 30000 \]

### Conclusion
The total number of examinees is \( N = 30000 \).

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