Q) Essel World is one of India’s largest amusement parks that offers a diverse range of thrilling rides, water attractions and entertainment options for visitors of all ages. The park is known for its iconic ‘‘Water Kingdom’’ section, making it a popular destination for family outings and fun-filled adventure. The ticket charges for the park are Rs. 150 per child and Rs. 250 per adult.
On a day, the cashier of the park found that 300 tickets were sold and an amount of Rs. 55,000 was collected.
Based on the above, answer the following questions :
(i) If the number of children visited be x and the number of adults visited be y, then write the given situation algebraically.
(ii) How many children visited the amusement park that day?
(iii) How many adults visited the amusement park that day?
(iv) How much amount will be collected if 250 children and 100 adults visit the amusement park?
Ans:
(i) algebraic expressions for the situations:
Situation 1:
No. of Children visited = x
and No. of adults visited = y
Also it is given that total 300 tickets were sold.
∴ No. children’s tickets sold + No. children’s tickets sold = total no. of tickets sold
∴ x + y = 300 ….. (i)
Situation 2:
Child ticket cost = Rs. 150 and No. of Children visited = x
∴ Amount collected by children’s tickets sale = No. of children x Cost of one child ticket = 150 x
Similarly, Adult ticket cost = Rs. 250 and No. of adults visited = y
∴ Amount collected by adults’ tickets sale = No. of adults x Cost of one adult ticket = 250 y
∴ Total Amount collected by all tickets sale = Amount collected by children’s tickets sale + Amount collected by adults’ tickets sale
∴ Total Amount = 150 x + 250 y
Given that Amount collected is Rs. 55,000
∴ 150 x + 250 y = 55,000
∴ 3 x + 5 y = 1100 ……… (ii)
(ii) Number of children visited the amusement park:
To solve for values of x & y, we multiply equation (i) by 5 and subtract equation (i) from it:
5 (x + y) – (3 x + 5 y) = 5 (300) – 1100
5 x + 5 y – 3 x – 5 y = 1500 – 1100
2 x = 400
x = 
x = 200
Therefore, 200 children visited the amusement park.
(iii) Number of adults visited the amusement park:
By substituting this value of x in equation (i), we get:
x + y = 300
200 + y = 300
y = 300 – 200
y = 100
Therefore, 100 adults visited the amusement park.
(iv) Amount collected by visit of 250 children and 100 adults:
New value of x (number of children visited) = 250
Cost of one child ticket = 150
∴ Amount collected by children’s tickets sale = No. of children x Cost of one child ticket = 250 x 150 = Rs. 37,500
New value of y (number of adults visited) = 100
Similarly, Adult ticket cost = Rs. 250
∴ Amount collected by adults’ tickets sale = No. of adults x Cost of one adult ticket = 100 x 250 = Rs. 25,000
∴ Total Amount collected by all tickets sale = Amount collected by children’s tickets sale + Amount collected by adults’ tickets sale
∴ Total Amount = 37,500 + 25,000 = Rs. 62,500
Therefore, Rs. 62,500 collected by visit of 250 children and 100 adults:
Please press the “Heart”, if you liked the solution.