Question

The organisers of an essay competition decide that a winner in the competition gets a prize of Rs. $100$ and a participant who does not win gets a prize of Rs. $25$. The total prize money distributed is Rs. $3000$. Find the number of winners, if the total number of participants is $63$.

• A. $14$
• B. $16$
• C. $19$
• D. $12$

Answer 1

The correct option is C $19$

Let x be the number of the winners. So, the number of participants who does not win $(63-x)$.

Prize money given to $x$ winners = Rs. $(100\times x)=$ Rs. $100x$
and prize money given to $(63-x)$ participants = Rs. $25(63-x)$

Given, total prize money distributed = Rs. $3000$
$\therefore 100x+25(63-x)=3000$
$\Rightarrow 4x+(63-x)=120$ ...[On dividing both sides by 25]

$\Rightarrow 3x+63=120$
$\Rightarrow 3x=120-63$ ...[Transposing 63 to RHS]

$\Rightarrow 3x-57\Rightarrow x=\frac{57}{3}=19$

$\therefore$ The number of winners is $19$.