MBApyq

Football Match Winning Percentages

XAT 2023 · Quantitative Ability & Data Interpretation · Medium · Percentages

All XAT 2023 questionsMore Percentages questionsAll XAT QADI

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.

  1. A.

    50

  2. B.

    40

  3. C.

    30

  4. D.

    Cannot be determined, as the value of n is not given

  5. E.

    60

Answer

A

Explanation

Let total initial matches = mm, wins = 0.4m0.4m. Condition 1: 0.4m+nm+n=0.5  ⟹  0.4m+n=0.5m+0.5n  ⟹  0.1m=0.5n  ⟹  m=5n\frac{0.4m + n}{m + n} = 0.5 \implies 0.4m + n = 0.5m + 0.5n \implies 0.1m = 0.5n \implies m = 5n. Condition 2: 0.5(m+n)+15m+n+15=0.6\frac{0.5(m+n) + 15}{m + n + 15} = 0.6. Substitute m=5n  ⟹  m+n=6nm = 5n \implies m+n = 6n. 3n+156n+15=0.6  ⟹  3n+15=3.6n+9  ⟹  0.6n=6  ⟹  n=10\frac{3n + 15}{6n + 15} = 0.6 \implies 3n + 15 = 3.6n + 9 \implies 0.6n = 6 \implies n = 10. m=5×10=50m = 5 \times 10 = 50.

Related Percentages questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace