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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

Updated On: Jan 15, 2026
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Solution and Explanation

Let x represent the count of matches concluded. Considering the subsequent 10 matches:

  • A total of one goal results in an average of 0.15 goals per match.
  • A total of two goals results in an average of 0.2 goals per match.

Let \( G \) denote the cumulative goals scored in the initial \( x \) matches.

Following an additional 10 matches, the total match count is:
\[ x + 10 \]

Scenario 1: One goal scored in the next 10 matches

Cumulative goals: \( G + 1 \)
Average goals per match: \( \frac{G + 1}{x + 10} = 0.15 \)

Scenario 2: Two goals scored in the next 10 matches

Cumulative goals: \( G + 2 \)
Average: \( \frac{G + 2}{x + 10} = 0.2 \)

Subtracting the equations:

\[ \frac{G + 2}{x + 10} - \frac{G + 1}{x + 10} = 0.2 - 0.15 \] \[ \frac{(G + 2) - (G + 1)}{x + 10} = 0.05 \] \[ \frac{1}{x + 10} = 0.05 \]

Calculating \( x \):

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

Conclusion:

The number of matches previously played is: 10.

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