Matches won by a team in tournament

CAT 2021 Slot 3 · QA · Easy · Percentages

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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

Explanation

Matches played = 40, won = 30%×40=1230\% \times 40 = 12.

Let remaining matches be RR. If they win 60% of RR, overall win rate is 50%: 12+0.6R40+R=0.5  ⟹  12+0.6R=20+0.5R  ⟹  0.1R=8  ⟹  R=80\frac{12 + 0.6R}{40 + R} = 0.5 \implies 12 + 0.6R = 20 + 0.5R \implies 0.1R = 8 \implies R = 80

If they win 90% of the remaining matches: Total matches won=12+0.9(80)=12+72=84\text{Total matches won} = 12 + 0.9(80) = 12 + 72 = 84.

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