Now, the scores in the table are the cumulative scores. We can easily see which recruits did not participate in which round from the fact that the cumulative scores do not change for a particular person in a particular round. For example, D did not participate in the first round, A did not participate in round 3, B did not participate in round 4, C did not participate in round 2 and E did not participate in round 5.
Let us assume that every round lasts for ‘x’ minutes and by the end of 5th round, each recruit shall have shot for 4x minutes. Now, the average cumulative score for A after round 5 is 60.4 meaning that the total score is = 60.4 * 4x = 241.6x and so on for other teams also.
Now, it can be deduced from observation that the maximum score by any recruit shall be in a round where the cumulative score has seen the maximum jump. So, the possible candidates are:
- A in round 5
- B in round 2
- C in round 3
- E in round 3
D is not valid because its score is decreasing in most of the rounds.
Let’s evaluate these cases:
- Now, at the end of round 5, the score of A is 241.6 and his time was 3x at the end of round 4 so, the score at the end of round 4 = 54.4 * 3x making the score for round 5 for A as = 78.4x
- At the end of round B, the score of B = 146x and the score = 67.2x at the end of round one. So, the score in round 2 = 78.8x
- Similarly, for C, the score in round 3 = 78.2x
- Score for E in round 3 = 69.6x
Hence, it is clear that the maximum score is for B in round 2 = 78.8x and the nearest integral score is if x is a multiple of 5 giving the maximum score as = 394