A certain amount is distributed equally among certain boys. If there were 5 boys more each would have received Rs. 8

Answer: 20 boys and Rs. 800 distributed

Let there be \(x\) boys, each getting Rs. \(y\). Amount = \(xy\).

5 more boys, Rs. 8 less each:

\[(x + 5)(y - 8) = xy \Rightarrow -8x + 5y = 40 \quad\text{(1)}\]

4 fewer boys, Rs. 10 more each:

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

Multiply (1) by 4 and (2) by 5: \(-32x + 20y = 160\) and \(50x - 20y = 200\). Adding: \(18x = 360 \Rightarrow x = 20\).

From (1): \(-160 + 5y = 40 \Rightarrow y = 40\).

Amount = 20 × 40 = Rs. 800.

Check: 25 boys get Rs. 32 each (800); 16 boys get Rs. 50 each (800).