Karan ranked 25th from the top and 58th from the bottom in his class. How many…

Concept:

When one person’s position in a line-up of n people is given both from the top and from the bottom, the two counts overlap only at that person’s own position. So the total number of people equals (rank from the top) + (rank from the bottom) − 1 — the “−1” removes the double count of the person themselves.

Application:

1. Karan’s rank from the top = 25, so 24 students stand above him.

2. Karan’s rank from the bottom = 58, so 57 students stand below him.

3. Total students = (students above) + (Karan himself) + (students below) = 24 + 1 + 57 = 82.

4. Equivalently, using the formula: total = 25 + 58 − 1 = 82.

Cross-check:

Both routes — the direct above/self/below count and the top+bottom−1 formula — agree on 82, confirming there are 82 students in Karan’s class.