Question

In a writing competition, it is decided that a winner will get a prize of 500 and a participant who does not win will get a prize of 100. The total prize money distributed is 10,000. Find the number of winners, if the total number of participants is 36.With steps for grade 8th cbse​

Answer 1

Given :

In a writing competition, it is decided that a winner will get a prize of 500 and a participant who does not win will get a prize of 100. The total prize money distributed is 10,000.

To find :

• Find the number of winners, if the total number of participants is 36.

Solution :

• Conditions

★ Winner will get a prize of Rs.500

★ Participant who does not win will get prize of Rs.100

Now,

• Total prize money distributed = Rs10000
• Total number of participant = 36

Consider the number of winner be x and the number of participants who did not win be y

• According to the question

Winners+participant who didn't win = 36

• x + y = 36 ----(i)

Winners × Rs.500 + participants who did not win × Rs.100 = Rs.10000

• 500x + 100y = 10,000

→ 100(5x + y) = 10000

→ 5x + y = 10000/100

→ 5x + y = 100 ---(ii)

• Subtract both the equations

→ x + y - (5x + y) = 36 - 100

→ x + y - 5x - y = - 64

→ x - 5x = - 64

→ - 4x = - 64

→ x = 64/4

→ x = 16

• Put the value of x in eqⁿ 1

→ x + y = 36

→ 16 + y = 36

→ y = 36 - 16

→ y = 20

•°• Number of winners = x = 16

•°• Number of who did not win = y = 20

Answer 2

Given :-

In a writing competition, it is decided that a winner will get a prize of 500 and a participant who does not win will get a prize of 100. The total prize money distributed is 10,000

To Find :-

Number of winners

Solution :-

Let the winners be x

No. of participate who lose = (36 - x)

Money given = 500x

Price to the people who does not win = 100(36 - x) = 3600 - 100x

10,000 = 500x + 3600 - 100x

10,000 = 400x + 3600

10,000 - 3600 = 400x

6400 = 400x

6400/400 = x

16 = x

Hence,

Number of winner is 16