Averages , Ratio and Proportion Question 1 - CAT 2021
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:
Step-by-Step Explanation
- Analyze the initial metrics:
Initial matches played = 40.
Initial wins = 30% of 40 = 12 matches.
Let the number of remaining matches be x.
- Apply the Alligation Framework:
The 40 initial matches (with a 30% win rate) are mixed with x remaining matches (with a 60% win rate) to produce an overall average win rate of 50%.
40/x = (60 − 50)/(50 − 30)
40/x = 10/20
40/x = 1/2
x = 40 × 2 = 80 remaining matches
- Calculate the final targeted wins:
If the team wins 90% of these 80 remaining matches, the new wins from this segment will be:
New Wins = 90% of 80 = 72 matches
Total Wins = 12 (initial) + 72 (new)
= 84 matches
Correct Option: C
💡 FundaMakers Tip:
Mixture alligations can bypass linear algebraic fractions entirely. Recognizing that the distance from 30% to 50% is double the distance from 60% to 50% reveals that the remaining match pool must be exactly twice the size of the initial match pool (40 × 2 = 80).