In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his geography paper and 2 more marks for his History paper, his average per paper would have been 65, then the number of papers in the examination are

Options

A. 8
B. 9
C. 10
D. 11

Answer

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

### Step 1: Define the Variables
Let \( x \) be the number of papers in the examination.

### Step 2: Calculate the Total Marks
The average marks per paper is given as 63. Therefore, the total marks obtained by the pupil for \( x \) papers can be calculated as:
\[ \text{Total Marks} = 63x \]

### Step 3: Adjust the Marks for Geography and History
According to the problem, if the pupil had obtained 20 more marks in Geography and 2 more marks in History, the new total marks would be:
\[ \text{New Total Marks} = 63x + 20 + 2 = 63x + 22 \]

### Step 4: Set Up the New Average Equation
With the new total marks, the average marks per paper would be 65. Thus, we can set up the equation:
\[ \frac{63x + 22}{x} = 65 \]

### Step 5: Clear the Denominator
To eliminate the fraction, multiply both sides of the equation by \( x \):
\[ 63x + 22 = 65x \]

### Step 6: Rearrange the Equation
Now, rearranging the equation gives:
\[ 65x - 63x = 22 \]
\[ 2x = 22 \]

### Step 7: Solve for \( x \)
Dividing both sides by 2 yields:
\[ x = 11 \]

### Conclusion
The number of papers in the examination is \( \boxed{11} \).

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