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Some cricketers were to be selected for the national cricket team from a group of probables. They were given ranks after undergoing various rounds of trials. Each cricketer had to go through a fitness test before the trials and only those who passed the fitness test could participate in the trials. After the trials, Pawan was ranked eleventh from the top and Ujjwal, who was seven ranks below Pawan, was forty-third from the bottom. If the ratio of the number of cricketers who passed the fitness test to those who did not was 20:7, how many cricketers were in the original list of probables?
  • a)
    108
  • b)
    84
  • c)
    81
  • d)
    54
  • e)
    None of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Some cricketers were to be selected for the national cricket team from...
Since Ujjwal was ranked seven places below Pawan, Ujjwal’s rank from the top = 11 + 7 = 18
Thus, Ujjwal was eighteenth from the top and forty-third from the bottom.
Number of cricketers that appeared for the trials = 18 + 43 - 1 = 60
Only the cricketers that passed the fitness test appeared for the trials.
Hence, option 3.
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Most Upvoted Answer
Some cricketers were to be selected for the national cricket team from...
Given information:
- Pawan is ranked eleventh from the top.
- Ujjwal is seven ranks below Pawan and is forty-third from the bottom.
- The ratio of cricketers who passed the fitness test to those who did not is 20:7.

Approach:
To solve this problem, we will first find the total number of cricketers who passed the fitness test and then use the given information to find the total number of cricketers in the original list of probables.

Solution:
Let's assume the total number of cricketers who passed the fitness test is 20x and the total number of cricketers who did not pass the fitness test is 7x.

Finding the rank of Ujjwal:
Since Pawan is ranked eleventh from the top and Ujjwal is seven ranks below Pawan, we can calculate Ujjwal's rank as follows:
Rank of Ujjwal = Rank of Pawan + 7 = 11 + 7 = 18

Finding the total number of cricketers:
To find the total number of cricketers, we need to add the number of cricketers ranked above Ujjwal and the number of cricketers ranked below Ujjwal.
Number of cricketers ranked above Ujjwal = 18 - 1 = 17
Number of cricketers ranked below Ujjwal = 43 - 1 = 42

Total number of cricketers = Number of cricketers ranked above Ujjwal + Number of cricketers ranked below Ujjwal + 1 (Ujjwal himself)
Total number of cricketers = 17 + 42 + 1 = 60

Finding the value of x:
We know that the ratio of cricketers who passed the fitness test to those who did not is 20:7.
Therefore, (20x)/(7x) = Total number of cricketers who passed the fitness test/Total number of cricketers who did not pass the fitness test = 20/7

Solving the above equation, we get:
20x = 7x
13x = 0
x = 0

Conclusion:
Since the value of x is 0, it means that there are no cricketers who passed the fitness test. But this contradicts the given information that some cricketers passed the fitness test. Therefore, this situation is not possible.

Hence, the given information is inconsistent or contradictory.
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