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
Explanation:
Let the number of matches played so far be ‘b’ and the goals scored in these ‘n’ matches be ‘g’.
Now if 1 goal is scored in next 10 matches
⇒ g + 1 = (n + 10) × 0.15
⇒ g = 0.15n + 1.5 …(1)
If 2 goals are scored in next 10 matches
⇒ g + 2 = (n + 10) × 0.2
⇒ g = 0.2n + 1 …(2)
Solving (1) and (2) we get,
n = 10
Hence, 10.
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