CAT 2021 Slot 3 QA Q14 Percentages & Profit-Loss

Question 14 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

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
  1. A
    86
  2. B
    84
  3. C
    78
  4. D
    80

Answer: (B) 84 Percentages & Profit-Loss MCQ

Solution

  1. Won so far \(= 0.3 \times 40 = 12\). Let \(r\) matches remain.
  2. \(12 + 0.6r = 0.5(40 + r) \Rightarrow 0.1r = 8 \Rightarrow r = 80\).
  3. Winning 90% of 80: total wins \(= 12 + 72 = 84\).

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