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CAT 2021 Slot 3 — QA Question 13

PercentageEasy

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

Answer & solution

  • A

    78

  • 84

  • C

    80

  • D

    86

Solution

Easy

First fix the number of remaining matches using the 50%50\% overall condition with the 60%60\% win rate. Then recompute the total wins under the 90%90\% scenario.

1

Wins so far. Of 4040 matches, 30%30\% are won.

Won=0.30×40=12\begin{aligned} &\text{Won} = 0.30\times 40 = 12 \end{aligned}
2

Find the remaining matches nn. Winning 60%60\% of the remaining nn makes the overall rate exactly 50%50\%.

12+0.6n=12(40+n)(overall win=50%)⇒ 24+1.2n=40+n⇒ 0.2n=16⇒ n=80\begin{aligned} &12 + 0.6n = \tfrac12(40 + n) \quad\text{(overall win}=50\%)\\ &\Rightarrow\ 24 + 1.2n = 40 + n\\ &\Rightarrow\ 0.2n = 16\\ &\Rightarrow\ n = 80 \end{aligned}
3

Now win 90%90\% of those 8080. Add the new wins to the 1212 from step 1.

New wins=0.90×80=72⇒ Total wins=12+72=84\begin{aligned} &\text{New wins} = 0.90\times 80 = 72\\ &\Rightarrow\ \text{Total wins} = 12 + 72 = 84 \end{aligned}
8484
CAT 2021 Slot 3 QA Q13: In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining mat — Solution | TheCATExam