Some amount is distributed equally among some boys. If 10 boys were more each would get Rs. 2 less and each would get Rs. 6 more if 15 boys were less. Find the amount distributed and the number of boys. Ans. 40 boys and Rs. 400.
Answer: 40 boys and Rs. 400 distributed
Let there be \(x\) boys, each getting Rs. \(y\). Amount = \(xy\).
10 more boys, Rs. 2 less each:
\[(x + 10)(y - 2) = xy \Rightarrow -2x + 10y = 20 \Rightarrow x = 5y - 10 \quad\text{(1)}\]
15 fewer boys, Rs. 6 more each:
\[(x - 15)(y + 6) = xy \Rightarrow 6x - 15y = 90 \Rightarrow 2x - 5y = 30 \quad\text{(2)}\]
Substitute (1) in (2): \(10y - 20 - 5y = 30 \Rightarrow y = 10\), so \(x = 40\).
Amount = 40 × 10 = Rs. 400.
Check: 50 boys get Rs. 8 each (400); 25 boys get Rs. 16 each (400).
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