Students were standing in rows for P.T exercises. If 4 students were less in each row, 10 more rows were required and

Answer: 800 students

Let there be \(x\) students in each row and \(y\) rows. Total students = \(xy\).

4 fewer per row needs 10 more rows:

\[(x - 4)(y + 10) = xy \Rightarrow 10x - 4y = 40 \Rightarrow 5x - 2y = 20 \quad\text{(1)}\]

5 more per row reduces rows by 8:

\[(x + 5)(y - 8) = xy \Rightarrow -8x + 5y = 40 \quad\text{(2)}\]

Multiply (1) by 5 and (2) by 2: \(25x - 10y = 100\) and \(-16x + 10y = 80\). Adding: \(9x = 180 \Rightarrow x = 20\).

From (1): \(100 - 2y = 20 \Rightarrow y = 40\).

Students = 20 × 40 = 800.

Check: 16 × 50 = 800 and 25 × 32 = 800.