Neena ranks fifth in a class. Seema is eighth from the last. If Tushar is…

Concept

In rank/order puzzles, three conversions are used repeatedly: a rank stated as "p places after" someone at rank r becomes rank r + p; a rank given as k-th from the last, in a class of N students, converts to rank N − k + 1 from the top; and a person exactly midway between two ranks r1 and r2 sits at rank (r1 + r2) / 2.

Application

1. Neena's rank from the top is 5.

2. Tushar is sixth after Neena, so his rank from the top is 5 + 6 = 11.

3. Tushar is exactly midway between Neena and Seema, so 11 = (5 + S) / 2, where S is Seema's rank from the top; solving gives S = 17.

4. Seema is eighth from the last, so in a class of N students her rank from the top is N − 8 + 1, that is N − 7.

5. Setting the two expressions for Seema's rank equal: N − 7 = 17, so N = 24.

Cross-check

With N = 24, Seema's rank from the last works out to 24 − 17 + 1 = 8, matching the given data, and the midpoint of Neena's rank (5) and Seema's rank (17) is (5 + 17) / 2 = 11, matching Tushar's rank.

Result

So the class has 24 students.