Title: 2021 Slot 1 Quant: Analyzing a Strategic Indian Game
Content: Detailed Solutions and Explanations
Problem Statement (Hypothetical Example):
In a strategic Indian game called Kho-Kho, players compete in teams. Each team has 10 players, and the game lasts for 20 rounds. A player earns 3 points for a win, 1 point for a draw, and 0 for a loss. A team’s total score is the sum of its players’ points. If Team A’s average score per player is 12 points, and Team B’s total score is 15% higher than Team A’s, what is the ratio of Team B’s total score to Team A’s total score?
Solution:
Step 1: Calculate Team A’s Total Score
Team A has 10 players.
Average score per player = 12 points.
Total score for Team A = ( 10 \times 12 = 120 ) points.
Step 2: Determine Team B’s Total Score
Team B’s score is 15% higher than Team A’s.
Total score for Team B = ( 120 + (0.15 \times 120) = 120 \times 1.15 = 138 ) points.
Step 3: Compute the Ratio
Ratio of Team B’s score to Team A’s score = ( \frac{138}{120} ).
Simplify: Divide numerator and denominator by 6 → ( \frac{23}{20} ).
Final Answer:
The ratio is ( \frac{23}{20} ) or ( 23:20 ).
Key Concepts Applied:
Average Calculation: Total score = average × number of players.
Percentage Increase: ( \text{New Value} = \text{Original} \times (1 + \text{Percentage}) ).
Ratio Simplification: Divide numerator and denominator by their greatest common divisor (GCD).
Verification:
Team A: ( 10 \times 12 = 120 ).
Team B: ( 120 \times 1.15 = 138 ).
Ratio: ( \frac{138}{120} = \frac{23}{20} ).
Similar Problems for Practice:
If Team C’s score is 25% of Team B’s, find its total score.
Solution: ( 138 \times 0.25 = 34.5 ).
A player’s score increases by 20% from 10 points. What is the new score?
Solution: ( 10 \times 1.2 = 12 ).
Let me know if you need further clarification or additional examples!
Note: The problem above is a hypothetical example tailored to the theme of strategic Indian games. Adjustments can be made for specific exam formats or game rules.
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