Question

On a particular day, 50000 people attended a Cricket Test Match between India and Australia in Sydney Cricket Ground. Let x be the number of adults attended the cricket match and y be the number of children attended the cricket match. Cost of an adult ticket was ₹ 1000 while cost of a child ticket was ₹ 200. On that day Revenue earned by selling all 50,000 tickets, was ₹ 4,20,00,000. Find how many adults and how many children attended the cricket match?

Answer 1

Given:

Total people = 50,000

Adult ticket price = ₹ 1000

Child ticket price = ₹ 200

Total revenue = ₹ 4,20,00,000

Let,

x = Number of adults

y = Number of children

Step 1: Form the equations:

(i) Total people

x + y = 50000

(ii) Total revenue

1000x + 200y = 4,20,00,000

Step 2: Simplify the revenue equation:

Divide the whole equation by 100:

10x + 2y = 420000

Divide by 2:

5x + y = 210000 

Step 3: Solve the two equations:

We have;

1. x + y = 50000

2. 5x + y = 210000

Subtract (2) from (1):

(x + y) − (5x + y) = 50000 − 210000

−4x = −160000

x = `(-160000)/-4`

x = 40000

Substituting value of x in (2),

5x + y = 210000

5(40000) + y = 210000

200000 + y = 210000

y = 210000 − 200000

y = 10000

∴ Number of adults who attended the match is 40000 and the number of children who attended is 10000.