In a reality show, two judges independently provided marks based on the performance of the participants. If the marks provided by the second judge are given by y= 1+ x, where x is the marks provided by the first judge. Then for a participant
Step-by-step Solution:
To solve this problem, we need to analyze how the relationship between the marks given by the two judges affects the final ranking of the participants.
The problem states that if the first judge gives marks 'x', the second judge gives marks 'y', according to the formula:
y = 1 + x
This means that for every participant, Judge 2's score is always exactly one point higher than Judge 1's score.
A participant's rank is determined by their score relative to the scores of all other participants. The person with the highest score gets rank 1, the second highest gets rank 2, and so on.
Let's consider two participants, P1 and P2.
If Judge 1 ranks P1 higher than P2, it means x1 > x2. If we add 1 to both sides of this inequality, the relationship remains the same: x1 + 1 > x2 + 1. This means y1 > y2, so Judge 2 will also rank P1 higher than P2.
Since adding a constant value to every participant's score does not change their relative order, the final ranking given by both judges will be identical.
Based on a logical analysis of how ranking works, the ranks given by both judges for any participant will be the same. This would make option D the correct answer.