CAT 2021 Slot 2 QA Question 6: In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0

Question

In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0

Accepted Answer

Let the number of matches already played be $m$, and let the number of goals already scored be $g$.

$\dfrac{g+1}{m+10}=0.15=\dfrac{3}{20}$
$\dfrac{g+2}{m+10}=0.2=\dfrac{1}{5}$

Subtract the first equation from the second.
$\dfrac{1}{m+10}=\dfrac{1}{5}-\dfrac{3}{20}=\dfrac{1}{20}$
$m+10=20$
$m=10$