Question

Who belongs to Punjab?

• A. A
• B. B
• C. C
• D. E
• A. 16
• B. 8
• C. 40
• D. 32
• A. 20
• B. 36
• C. 24
• D. Cannot be determined

Answer 1

The Correct Option is D

To determine who belongs to Punjab, let us analyze the problem step by step, starting with the given constraints:

1. Total runs possible: 96, 112, 64, 72, 80.
2. Each batsman's runs per ball is an integer and not more than 4.
3. The number of balls faced by each is a multiple of 4, between 16 and 36.

Given Information:

1. The batsman of team Mumbai scored 24 more than C.
2. The difference in runs between Bangalore and Rajasthan batsmen is half the difference between D and E's runs.
3. No one scored fewer runs per ball than the batsman who scored 16 runs less than the team Kolkata batsman's score.
4. B faced the least number of balls and scored 8 runs more than a batsman not in team Bangalore. E is not from Mumbai.

Steps:

1. Identify all possible combinations of runs based on balls faced and ensure runs per ball is an integer ≤ 4.
2. Assign scores based on these combinations to satisfy constraint 1. Let C's score be x, Mumbai's score = x + 24.
3. Apply constraint 2: Let Bangalore's score be y, and Rajasthan's score z. So, y - z = (D’s score - E's score) / 2.
4. Apply constraint 3 regarding runs scored differences.
5. Identify a valid combination based on points above that satisfy B's criteria (scoring 8 more than a player not from Bangalore).

Solution:

Based on the logical deductions above, and further narrowing within these constraints:

• By constraint 4, B inconsistently shows exclusions but consistently leads us to valid scoring sets for the teams that allow options examination and player E's exclusion from Mumbai.
• Using the filtration, E must belong to a team other than Mumbai, in context individualized through C, D, and finalized consideration for other scores and hints.
• Ultimately, based on exclusions and pattern context compliance given all initial setups and constraints logic:

Batsman	Team
E	Punjab

Answer 2

To solve this problem, we need to determine the scores of the batsmen of team Kolkata and team Rajasthan and find their difference.

1. Let's analyze the given information: We have five batsmen A, B, C, D, and E belonging to different teams. The runs scored are among 96, 112, 64, 72, and 80.
2. From the clue: "The total runs scored by the batsman of team Mumbai is 24 more than that scored by C." Since all scores are unique, C can score 72. Hence, the batsman of team Mumbai scores 96. 
3. From the second clue: "The difference between the runs scored by the batsmen of teams Bangalore and Rajasthan is half the difference between the runs scored by batsmen D and E." This means D and E must have the runs out of which one is the maximum (112) and one is the minimum (64). If D = 112 and E = 64, then difference D - E = 48.
4. For the clue "B faced the least number of balls and scored 8 runs more than a batsman, who is not a player of team Bangalore," B's runs are 72 (96, 72, 80 are possibilities for being 8 more runs), B must have scored 80 runs.
5. From the clue: "No one scored less runs per ball than the batsman who scored 16 runs less than that scored by the batsman of team Kolkata." Team Kolkata cannot score the minimum, which is 64, so team Kolkata scored 80 and team Rajasthan, owing to the unique aggressive sorting, gets 64.
6. Therefore, the scores are:
- Team Kolkata: 80
- Team Rajasthan: 64
7. The difference between the batsmen scores of team Kolkata and team Rajasthan is 80 - 64 = 16.

The difference is thus confirmed: 16.

Answer 3

Let's solve the problem using the given conditions. We have 5 players (A, B, C, D, E) and allocations of teams Rajasthan, Bangalore, Mumbai, Kolkata, and Punjab. Each batsman's runs and balls faced must pair with these allocations.
The runs scored are among 96, 112, 64, 72, and 80. The number of balls faced is a multiple of 4, between 16 and 36. Runs per ball is an integer, not more than 4. 

• Using condition 1, let runs of C be x. Mumbai scores x + 24.
• Using condition 2, let runs of Bangalore be y and Rajasthan be z. The difference, y - z, is half the difference between D and E's scores.
• Condition 3 indicates no one scores lower runs per ball than the player who scored 16 runs less than Kolkata. E is not in Mumbai.
• Condition 4 tells us B faced the fewest balls and scored 8 more than a player not in Bangalore.

Let’s assume possible allocations based on these clues:

1. Assign known values: Run totals: Mumbai = x + 24, Difference Relation: 2(y – z) = difference between D and E.
2. For Kolkota, 5" and "16" can be derived since x + 40 ≥ some team values imply x = 64.
3. Assign player runs — assume possible value allocations until all conditions satisfy.
    

Conclusion: Rajasthan player scores/yields 36 runs on 4 runs per ball condition. Therefore, balls faced = 36 / 4 = 9.
Yet, allocation gives original pre-shifted runs closer to 36. Thus, "Rajasthan balls = 36".