CAT 2021 Slot 3 - Quant Question 3

Question 3

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

Solution

Initially number of matches = 40 
Now matches won = 12 
Now let remaining matches be x 
Now number of matches won = 0.6x
Now as per the condition :
$$\frac{\left(12+0.6x\right)}{40+x}=\frac{1}{2}$$
24 +1.2x=40+x
0.2x=16
x=80
Now when they won 90% of remaining = 80(0.9) =72
So total won = 84


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Comments
Kamna Bisht

3 months, 3 weeks ago

30% of 40 will be 12
So 90 % of the raning matches would be an integer
In option the total number of winning is mentioned so
80-12=68
78-12=66
84-12=72
86-12=74
So 68,66,72 is the 90% of two matches as it will not be an integer
Ans 84

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