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The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible. (Solution is mentioned in the comments)
- 50
- 40
- 30
- Cannot be determined, as the value of n is not given
- 60
1 Replies
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Let the initial number of matches played be x.
By playing and winning n more matches, the winning percentage increases to 50%.
0.4x+n=0.5×(n+x)
0.4x+n=0.5n+0.5x
0.5n=0.1x
5n=x
By playing and winning 15 more matches, the winning percentage increases to 60%.
0.4x+n+15=0.6×(15+n+x)
3n+15=9+3.6n
0.6n=6
n=10
x=5n=50
