MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2024: question 36

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedPair of Linear Equations in Two Variables

Case Study – 1

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 mark
(ii)(a)
How many children visited the amusement park that day ?
2 marks
OR
(ii)(b)
How many adults visited the amusement park that day ?
2 marks
(iii)
How much amount will be collected if 250 children and 100 adults visit the amusement park ?
1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

One equation comes from counting tickets, the other from counting money.

Hint 2

Use substitution: write $x = 300 - y$ and put it into the money equation.

Hint 3

For (iii), multiply each number of visitors by its ticket price and add.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) Total number of tickets sold is 300: $x + y = 300$ ...(1)
½ mark
(i) Total amount collected at ₹150 per child and ₹250 per adult: $150 x + 250 y = 55000$ , i.e. $3 x + 5 y = 1100$ ...(2)
½ mark
(ii)(a) From (1), $x = 300 - y$ . Substituting in (2): $3 (300 - y) + 5 y = 1100 \Rightarrow 900 + 2 y = 1100 \Rightarrow y = 100$ .
1 mark
(ii)(a) So $x = 300 - 100 = 200$ . 200 children visited the park that day.
1 mark
(ii)(b) From (1), $x = 300 - y$ . Substituting in (2): $900 - 3 y + 5 y = 1100 \Rightarrow 2 y = 200$ .
1 mark
(ii)(b) So $y = 100$ . 100 adults visited the park that day. (Check: $150 (200) + 250 (100) = 30000 + 25000 = 55000$ ✓)
1 mark
(iii) Amount collected $= 250 \times 150 + 100 \times 250 = 37500 + 25000 =$ ₹62,500.
1 mark

Answer: (i) $x + y = 300$ , $150 x + 250 y = 55000$ ; (ii)(a) 200 children; (ii)(b) 100 adults; (iii) ₹62,500

Where the marks are

Writes $x + y = 300$ (½ mark)
Writes $150 x + 250 y = 55000$ (½ mark)
(ii)(a) Solves the pair of equations correctly to get 200 children (2 marks)
(ii)(b) Solves the pair of equations correctly to get 100 adults (2 marks)
(iii) Computes $250 \times 150 + 100 \times 250 = ₹62500$ (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 36

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables