Question

In a debate competition, there were 30 participants. The winners received a prize of rs.1500 each and those who didn't win, received prize money of rs.550 each . If rs.22,200 was distributed in total , find the number of winners.​

Answer 1

Given.

• Total number of participants is 30

• Winners received a prize money of Rs. 1500 each and those who didn't win received a prize money of Rs. 550 each.

• Total amount is Rs. 22200

To find.

• The number of winners.

Solution.

• Let the number of winners be x and the number of those who didn't win a prize is y.

• Then by the given conditions,
• x + y = 30 .....(1)
• 1500x + 550y = 22200 .....(2)

• From (1), we get: y = 30 - x and substituting in (2), we get
• 1500x + 550 (30 - x) = 22200
• or, 1500x + 16500 - 550x = 22200
• or, 950x = 5700
• or, x = 6

Answer.

• Total number of winners is 6.

Answer 2

Given :-

• In a debate competition, there were 30 participants.
• The winners received a prize of Rs. 1500 each and those who didn't win, received prize money of Rs. 550 each.
• If Rs. 22,200 was distributed in total.

To Find :-

• The number of winners.

Solution :-

• Let the number of winners be 'x'.
• Let the number of those who didn't win a prize be 'y'.

☆ Then by the given conditions,

$\bigstar\:\sf x + y = 30 - - - (i) \\ \\ \implies\boxed{\sf y = 30 - x}$

$\bigstar\:\sf1500x + 550y = 22200 - - - (ii)$

Substitute the value of y in equation (ii) we get,

$\implies \sf1500x + 550 \: (30 - x) = 22200 \\ \\ \implies \sf1500x + 16500 - 550x = 22200 \\ \\ \implies \sf1500x - 550x = 22200 - 16500 \\ \\ \implies \sf950x = 5700 \\ \\ \implies \sf x = \frac{\cancel{5700}}{\cancel{950}} \\ \\ \implies\underline {\boxed{ \purple {\sf x = 6}}}$

$\green{\therefore\underline { \sf Total \: number \: of \: winners \: is \: 6}}$