CAT 2021 Slot 3 · Quant · Question 14

CAT 2021 Slot 3 previous year question on Percentage, with the answer and a step-by-step solution.

PercentageArithmeticMultiple choiceEasy
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
Pick an option, then check.
Answer & solution

Answer: Option B

So far the team has won 30\% of 40, that is 12 matches.

Let r be the number of matches remaining. Winning 60\% of them gives an overall rate of 50\%:

\frac{12+0.6r}{40+r}=0.5, so 12+0.6r=20+0.5r, giving 0.1r=8 and r=80.

Now winning 90\% of those 80 gives 72 more wins, so the total is 12+72=84.

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