Question

If India reached the finals, then what is the minimum number of points it would have scored in the preliminary stage?

• A. 8
• B. 10
• C. 12
• D. 6
• A. 12
• B. 16
• C. 14
• D. 20
• A. 16
• B. 15
• C. 17
• D. 14

Answer 1

The Correct Option is A

Each team plays each of the other 2 teams 4 times → Total matches per team = \( 4 \times 2 = 8 \) matches.
Total matches in the tournament = \( 3 \text{ teams} \times 8 \div 2 = 12 \) matches.
Each win = 4 points, possibly +1 bonus → max per match = 5.
Total maximum possible points in the tournament = \( 12 \times 5 = 60 \). But if no bonus, max is \( 12 \times 4 = 48 \).
Suppose India reaches the finals with minimum points. Then it must be at 2nd place. So the other two teams’ scores must be higher/lower accordingly.
Try allocating total points minimally: Let Australia = 16 pts, India = 8 pts, Sri Lanka = remaining. Total = \( 16 + 8 + x = 48 \Rightarrow x = 24 \).
Now Sri Lanka cannot have 24 and still be below India — contradiction. Try India = 8, others = 20 and 20 → not possible. Try India = 8, Sri Lanka = 18, Australia = 22 → total = 48. Yes, valid if India 2nd by NRR.
Hence, \[ \boxed{8} \]

Answer 2

Since Sri Lanka is eliminated, it must finish 3rd, so its points must be less than the other two teams.
To maximize Sri Lanka’s points, let other two teams have just more than Sri Lanka. Try India = 15, Australia = 16, Sri Lanka = 14 → total = 45 → valid.
Try Sri Lanka = 16 → then both other teams need to be>16 = not possible with only 48 points total.
So maximum possible for 3rd placed team = \boxed{14}

Answer 3

To find minimum points for highest team (Australia), assume both other teams are just below.
Let India = 16, Sri Lanka = 15 → Total = \( 16 + 15 = 31 \), so Australia = 17 → total = 48 — valid.
If Australia had only 16, then another team could also have 16 → not unique max. So 17 is the minimum required to ensure highest points. \[ \boxed{17} \]