A cricket tournament had three teams– India, Australia and Sri Lanka– taking part in it. The format of the tournament was such that in the preliminary stage each of these teams would play the other teams four times.
Four points are awarded for a win and in case a team beats another team by a huge margin, it is given a bonus point in addition to the four points.
At the end of the preliminary stage, the top two teams, in terms of the points scored, reach the finals.
No match in the tournament ends in a tie and if two teams end up with the same number of points at the end of the preliminary stage, the team with the better net run rate is placed higher
If India reached the finals, then what is the minimum number of points it would have scored in the preliminary stage?
Show Hint
- 8
- 10
- 12
- 6
The Correct Option is A
Solution and Explanation
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, \[ \boxed{8} \]
If Sri Lanka was eliminated in the preliminary stage, then what is the maximum number of points it could have scored?
Show Hint
- 12
- 16
- 14
- 20
The Correct Option is C
Solution and Explanation
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}
If Australia had the highest number of points at the end of the preliminary stage, then at least how many points did it have?
Show Hint
- 16
- 15
- 17
- 14
The Correct Option is C
Solution and Explanation
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. \[ \boxed{17} \]
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