CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.
Question 14 : 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
Let the number of matches to be played be ‘x’
We are given that 40 matches are already played and 30% of them are won.
If 60% of the remaining matches are won, then the overall win percentage is 50%.
30% of 40 + 60% of x = 50% of (40 + x)
0.3 (40) + 0.6 (x) = 0.5 (40 + x)
12 + 0.6 (x) = 20 + 0.5 (x)
0.1 (x) = 8
x = 80
The number of matches to be played is 80.
If the team wins 90% of the remaining matches, it would win 90% of 80 = 72 matches.
Total matches won by the team
= 30% of 40 + 72
= 12 + 72 = 84
Choice B is the correct answer.
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