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

Answer 1

Correct Answer: 10

Let the number of matches already played be \( x \).  

Now, the player plays 10 more matches. Let’s analyze two scenarios:

1. Case 1: If the player scores 1 goal in these 10 matches, the new average becomes: \[ \text{Average} = 0.15 \]
2. Case 2: If the player scores 2 goals in these 10 matches, the new average becomes: \[ \text{Average} = 0.20 \]

So, scoring 1 additional goal increases the average from 0.15 to 0.20, which means an increase of:

\[ 0.20 - 0.15 = 0.05 \]

This increase of 0.05 in average due to 1 extra goal implies:

\[ \frac{1 \text{ goal}}{x + 10 \text{ matches}} = 0.05 \Rightarrow x + 10 = \frac{1}{0.05} = 20 \]

Hence, total matches after 10 more games = 20.

\[ \Rightarrow x = 20 - 10 = 10 \]

Final Answer:

Number of matches already played = 10