MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 36

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, 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

A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹ 50 and for each table is ₹ 200. The school spends ₹ 30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.

If the school rents 'x' chairs and 'y' tables, answer the following questions :

(i)
Write down the pair of linear equations representing the given information.
1 mark
(ii)(a)
Find the number of chairs and number of tables rented by the school.
2 marks
OR
(ii)(b)
If the school wants to spend a maximum of ₹ 27,000 on 300 items (tables and chairs), then find the number of chairs and tables it can rent.
2 marks
(iii)
What is maximum number of tables that can be rented in ₹ 30,000 if no chairs are rented ?
1 mark

Figure in the paper: A photograph of a classroom-style hall with rows of white tables and red and grey chairs arranged around them, with windows on the left. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

One equation counts the items and the other counts the money spent.

Hint 2

Divide the money equation by 50 to simplify it, then subtract the count equation to eliminate $x$ .

Hint 3

For (iii), all the money is spent on tables only.

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 items: $x + y = 300$
½ mark
(i) Total rent: $50 x + 200 y = 30000$ , i.e. $x + 4 y = 600$ (dividing by 50).
½ mark
(ii)(a) Subtract $x + y = 300$ from $x + 4 y = 600$ :
$3 y = 300 \Rightarrow y = 100$
1 mark
(ii)(a) $x = 300 - 100 = 200$
So the school rented 200 chairs and 100 tables.
1 mark
(ii)(b) Take the spending as ₹27,000 on 300 items:
$x + y = 300$ and $50 x + 200 y = 27000$ , i.e. $x + 4 y = 540$
1 mark
(ii)(b) Subtracting: $3 y = 240 \Rightarrow y = 80$ , so $x = 300 - 80 = 220$ .
It can rent 220 chairs and 80 tables.
1 mark
(iii) With no chairs, all ₹30,000 goes on tables at ₹200 each.
Number of tables $= \frac{30000}{200} = 150$
Maximum number of tables = 150.
1 mark

Answer: (i) $x + y = 300$ , $50 x + 200 y = 30000$ (i.e. $x + 4 y = 600$ ); (ii)(a) 200 chairs, 100 tables; (ii)(b) 220 chairs, 80 tables; (iii) 150 tables

Where the marks are

(i) Writes $x + y = 300$ (½ mark)
(i) Writes $50 x + 200 y = 30000$ (½ mark)
(ii)(a) Finds $y = 100$ (1 mark)
(ii)(a) Finds $x = 200$ (1 mark)
(ii)(b) Forms $x + 4 y = 540$ along with $x + y = 300$ (1 mark)
(ii)(b) Finds $x = 220$ and $y = 80$ (½ + ½ marks)
(iii) $30000 \div 200 = 150$ tables (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 paper2025 board paper, set 30/2/1 (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 2025: question 36

Hints

Step-by-step solution

Revise the chapter

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