Question

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.

Answer 1

Total sum of money = ₹3,000
Let the number of winners of ₹100 be x.
Total participants = 63
therefore no. of participant who does not win = 63 - x
According to the question,
$100\times x+25\times (63-x)=3000$
$\Rightarrow 100x+1575-25x=3000$
$\Rightarrow 75x+1575=3000$
$\Rightarrow 75x+1575-1575=3000-1575$ [Subtracting 1575 from both sides]
$\Rightarrow 75x=1425$
$\Rightarrow \frac{75x}{75}=\frac{1425}{75}$ [Dividing both sides by 75]
$x=19$
Hence, the number of winners is 19.