In a class, Pratik's rank from the top is 12 and Ramesh's rank from the bottom…
2023
In a class, Pratik's rank from the top is 12 and Ramesh's rank from the bottom is 27. If they interchange their positions, Pratik's rank becomes 18th from the top. Find the total number of persons in the class.
- A.
44
- B.
42
- C.
43
- D.
45
Attempted by 16 students.
Show answer & explanation
Correct answer: A
Let the total number of students be N.
Ramesh's rank from the bottom is 27, so his rank from the top = N - 27 + 1 = N - 26.
Pratik's original rank from the top is 12. After they interchange positions, Pratik becomes 18th from the top, so he must be at Ramesh's original position. Therefore:
Ramesh's original top rank = N - 26.
After interchange Pratik's rank = 18, so N - 26 = 18.
Solve: N = 18 + 26 = 44.
Final answer: 44 students.
Note: A common mistake is forgetting the +1 when converting a bottom rank to a top rank; remember top rank = N - (bottom rank) + 1.