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. $3,000$. Find the number of winners, if the total number of participants is $63$.

• A. $16$
• B. $19$
• C. $11$
• D. $15$

Answer 1

Answer: (B)

$19$

Let the number of winners $=x$.

$\therefore$ Amount of prize money $=100\times x=100x$.....(i)

Now the number of persons who don't win will be $=63-x$

$\therefore$ Amount of prize money $=25\times (63-x)$

$=1575-25x$

$\therefore$ By the given condition

$100x+1575-25x=3000$

$\Rightarrow 75x+1575=3000$

$\Rightarrow 75x=1425$

$\Rightarrow x=19$

So,the number of winners $=19$.