cat 2021 Question 14

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 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is

Accepted Answer

Let Total matches played be n and in initial n-10 matches his goals be x

so we get $\frac{1+x}{n}$ = 0.15

we get x+1 =0.15n (1)

From condition (2) we get :

$\frac{2+x}{n}$ = 0.15

we get x+2 = 0.2n (2)

Subtracting (1) and (2)

we get 1 =0.05n

n =20

So initially he played n-10 =10 matches

Question 14.

Question Explanation