Question

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 $65$. How many papers were there in the examination?

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is D $11$

Let the number of papers in the examination be $x$

Let the geography paper marks be $x_1$ and

the history paper marks be $x_2$

Given that the total average marks is $63$

Therefore, $63=\frac{x_1+x_2+\text{sum of the remaining papers}}{x}$

$x_1+x_2+\text{sum of the remaining papers}=63x$ -----(1)

Given that the geography paper marks is increased by $20$ and the history marks by $2$ then average becomes $65$

Therefore, $65=\frac{x_1+20+x_2+2+\text{sum of the remaining papers}}{x}$

$⟹x_1+x_2+\text{sum of the remaining papers}+22=65x$

$⟹63x+22=65x$ (from (1))

$⟹2x=22$

$⟹x=11$

Therefore, the number of papers in the examination is $11$