Q1. [4]
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 ₹150 per child and ₹250 per adult.
On a day, the cashier of the park found that 300 tickets were sold and an amount of ₹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. [1]
- (ii) How many children/adults visited the amusement park that day? [2]
- (iii) How much amount will be collected if 250 children and 100 adults visit the amusement park? [1]
Previously asked in CBSE board exam
2024 30/5/1 Q36
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
(i) The situation algebraically:
$$x + y = 300$$
$$150x + 250y = 55000$$
(ii) From equation (i): $x = 300 - y$
Substituting in equation (ii):
$$150(300 - y) + 250y = 55000$$
$$45000 - 150y + 250y = 55000$$
$$100y = 10000 \implies y = 100$$
So $x = 300 - 100 = 200$
200 children and 100 adults visited the park that day.
(iii) Amount collected = $150 \times 250 + 250 \times 100$
$$= 37500 + 25000 = ₹62,500$$
Source: Case Study passage, Essel World ticket problem.
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Explanation
- (i) Simply translate the two conditions (total tickets = 300, total amount = ₹55,000) into two linear equations. This is the standard "form the pair of equations" step.
- (ii) Use substitution method — the most straightforward approach here. Show all steps clearly for full 2-mark credit.
- (iii) Direct substitution of given values (250 children, 100 adults) into the fare formula. No equation-solving needed; just arithmetic.
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