In a competitive examination, the average marks obtained was 45. it was later discovered that there was some error in computerisation and the marks of 90 candidates had to be changed from 80 to 50 and the average came down to 40 marks. The total number of candidates who appeared in examination is

Options

A. 520
B. 550
C. 540
D. 560

Answer

To find the total number of candidates who appeared in the examination, we can follow these steps:

### Step 1: Define the variables
Let \( X \) be the total number of candidates who appeared in the examination.

### Step 2: Calculate the initial total marks
The average marks obtained by the candidates was 45. Therefore, the total marks obtained by all candidates can be calculated as:
\[ \text{Total Marks} = \text{Average} \times \text{Number of Candidates} = 45 \times X \]

### Step 3: Determine the change in marks for 90 candidates
It was discovered that the marks of 90 candidates were incorrectly recorded. Their marks changed from 80 to 50. The change in marks for each of these candidates is:
\[ \text{Change in Marks} = 80 - 50 = 30 \]
Thus, the total change in marks for 90 candidates is:
\[ \text{Total Change} = 90 \times 30 = 2700 \]

### Step 4: Calculate the new total marks
After correcting the marks, the new total marks will be:
\[ \text{New Total Marks} = \text{Old Total Marks} - \text{Total Change} = 45X - 2700 \]

### Step 5: Calculate the new average
After the correction, the average marks came down to 40. Therefore, we can express the new total marks as:
\[ \text{New Total Marks} = 40 \times X \]

### Step 6: Set up the equation
Now we can set up the equation based on the new total marks:
\[ 45X - 2700 = 40X \]

### Step 7: Solve for \( X \)
Rearranging the equation gives:
\[ 45X - 40X = 2700 \]
\[ 5X = 2700 \]
Now, divide both sides by 5:
\[ X = \frac{2700}{5} = 540 \]

### Conclusion
The total number of candidates who appeared in the examination is \( 540 \).

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