The organizers of an essay competition decide that a winner in the com

1.	The organizers 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.
Answer» Let the number of winners be x. Therefore, the number of participants who did not win will be 63 − x. Amount given to the winners = Rs (100 × x) = Rs 100x Amount given to the participants who did not win = Rs [25(63 − x)] = Rs (1575 − 25x) According to the given question, 100x + 1575 − 25x = 3000 On transposing 1575 to R.H.S, we obtain 75x = 3000 − 1575 75x = 1425 On dividing both sides by 75, we obtain 75x/75 = 1425/75 x = 19 Hence, number of winners = 19

The organizers 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.

Answer»

Let the number of winners be x. Therefore, the number of participants who did not win will be 63 − x.

Amount given to the winners = Rs (100 × x) = Rs 100x

Amount given to the participants who did not win = Rs [25(63 − x)] = Rs (1575 − 25x)

According to the given question,

100x + 1575 − 25x = 3000

On transposing 1575 to R.H.S, we obtain

75x = 3000 − 1575

75x = 1425

On dividing both sides by 75, we obtain

75x/75 = 1425/75

x = 19

Hence, number of winners = 19