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# 16.The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

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