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Question:

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.

Explanation:

Let the total matches played so far = m.
Number of matches won = 0.4m

After playing n more matches and winning all the matches, win rate becomes 50%.
Total matches played = m + n
Total matches won = 0.4m + n
⇒ 0.4m + n = 50% of (m + n)
⇒ 0.4m + n = 0.5m + 0.5n
⇒ 0.5n = 0.1m
⇒ m : n = 5 : 1
⇒ m = 5x and n = x ...(1)

After playing 15 more matches and winning all the matches, win rate becomes 60%
Total matches played = m + n + 15
Total matches won = 0.4m + n + 15
⇒ 0.4m + n + 15 = 60% of (m + n + 15)
⇒ 0.4m + n + 15 = 0.6m + 0.6n + 9
⇒ 0.4n + 6 = 0.2m
⇒ 0.4 × x + 6 = 0.2 × 5x
⇒ 0.4x + 6 = x
⇒ x = 10

∴ Matches played by Guava club so far = m = 5x = 50.

Hence, option (a).

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