In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be
Explanation:
Matches so far: Total played = 40 Won = 30% of 40 = 12
Let the number of remaining matches be ‘n’. The team wins 60% i.e., 0.6n matches.
There overall win percentage is 50% i.e., half
⇒ 12 + 0.6n = ½ (40 + n)
⇒ 24 + 1.2n = 40 + n
⇒ n = 80
Now, if the team wins 90% of these 80 remaining matches, they will win 90% of 80 = 72 more matches.
∴ Total matches won = 12 + 72 = 84
Hence, option (b).
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