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Answer :
Let the number of winners = x
Number of participants who do not win the prize = 63 – x
Amount won by winners = ₹ 100 × x = ₹ 100x
Amount won by losers = ₹ (63 – x) × 25 = ₹ (1575 – 25x)
As per the conditions given, we get
100x + 1575 – 25x = 3000
\(\Rightarrow\) 75x + 1575 = 3000
\(\Rightarrow\) 75x = 3000 – 1575 (transposing 1575 to RHS)
\(\Rightarrow\) 75x = 1425
\(\Rightarrow\) x = 1425 ÷ 75 (Transposing 75 to RHS)
\(\Rightarrow\) x = 19
Thus, the number of winners = 19