CAT 2021Slot 3QAQuestion & Solution
Question
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
Options
80
78
84
86
Solution
1. Concept Used
- Topic: Ratio and Proportion / Percentage
- Formula: $$\text{Overall Win %}= \frac{\text{Total Matches Won}}{\text{Total Matches Played}} \times 100$$
2. Calculation
The team has played 40 matches and won 30% of them, so matches won so far = ( 40 \times 0.30 = 12 ).
Let the number of remaining matches be ( x ). If they win 60% of remaining matches, wins from remaining = ( 0.6x ).
The condition for 50% overall win percentage gives us:
$$\frac{12 + 0.6x}{40 + x} = \frac{1}{2}$$
Cross-multiplying: ( 2(12 + 0.6x) = 40 + x )
$$24 + 1.2x = 40 + x$$
$$1.2x - x = 40 - 24$$
$$0.2x = 16 \implies x = 80$$
So the remaining matches = 80.
Now, if they win 90% of the remaining 80 matches:
$$\text{Wins from remaining} = 0.9 \times 80 = 72$$
$$\text{Total wins} = 12 + 72 = 84$$
3. Solution
Answer = Option C ✅
The total number of matches won by the team in the tournament will be 84.