In an exam, the average was found to be x marks. After deducting computational error, the average marks of 94 candidates got reduced from 84 to 64. The average thus came down by 18.8 marks. The numbers of candidates who took the exam were:

Options

A. 100
B. 90
C. 110
D. 105

Answer

To solve the problem step by step, we will follow the information provided in the question and use the average formula to find the number of candidates who took the exam.

### Step 1: Understand the given data
We know that:
- The average marks of 94 candidates was initially 84.
- After correcting a computational error, the average marks dropped to 64.
- The average thus came down by 18.8 marks.

### Step 2: Calculate the total marks before and after the error
We can calculate the total marks before and after the error using the formula:
\[ \text{Total Marks} = \text{Average} \times \text{Number of Candidates} \]

**Before the error:**
\[ \text{Total Marks (before)} = 84 \times 94 \]

**After the error:**
\[ \text{Total Marks (after)} = 64 \times 94 \]

### Step 3: Calculate the reduction in total marks
Now, we can find the reduction in total marks:
\[ \text{Reduction} = \text{Total Marks (before)} - \text{Total Marks (after)} \]
\[ \text{Reduction} = (84 \times 94) - (64 \times 94) \]
\[ \text{Reduction} = 94 \times (84 - 64) \]
\[ \text{Reduction} = 94 \times 20 \]

### Step 4: Set up the equation with the average reduction
We know from the problem that the average reduction is given as 18.8 marks, and we can express this as:
\[ \text{Reduction} = 18.8 \times n \]
where \( n \) is the number of candidates who took the exam.

### Step 5: Equate the two expressions for reduction
Now we can set the two expressions for reduction equal to each other:
\[ 94 \times 20 = 18.8 \times n \]

### Step 6: Solve for \( n \)
To find \( n \), we can rearrange the equation:
\[ n = \frac{94 \times 20}{18.8} \]

### Step 7: Calculate \( n \)
Now we can perform the calculation:
\[ n = \frac{1880}{18.8} \]
\[ n = 100 \]

### Conclusion
The number of candidates who took the exam is **100**.