MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 36

From the official CBSE sample question paper for 2026-27, 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

A student entrepreneur started a company that manufactures sanitizers in two sizes – small and large. The cost of a small bottle of sanitizer is ₹10 and that of a large bottle is ₹15. In June, the company sold 1000 bottles and recorded a total sale of ₹12,750. Seeing the increased demand, the company decided to increase the price of both sanitizer bottles by ₹2 each. In the next month, the company sold 2500 bottles and recorded a total sale of ₹34,250.
Based on the above information, answer the following questions:

(i)
Form a linear equation in two variables representing the sale for June.
1 mark
(ii)
Form a linear equation in two variables representing the sale for July.
1 mark
(iii)
(A) How many sanitizer bottles of each type were actually sold in June?
2 marks
OR
(iii)
(B) How many sanitizer bottles of each type were sold in July?
2 marks

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Let $x$ and $y$ be the numbers of small and large bottles; total sale = price × number for each size, added together.

Hint 2

In July each price goes up by ₹2, so the prices become ₹12 and ₹17.

Hint 3

Pair the sales equation with the total-bottle equation and solve by substitution.

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.

Let $x$ = number of small bottles and $y$ = number of large bottles.
(i) June prices are ₹10 and ₹15, and total sale is ₹12750:
$10 x + 15 y = 12750$ , i.e. $2 x + 3 y = 2550$
1 mark
(ii) July prices are ₹12 and ₹17, and total sale is ₹34250:
$12 x + 17 y = 34250$
1 mark
(iii)(a) For June:
- $x + y = 1000$ ...(1)
- $10 x + 15 y = 12750$ ...(2)
1 mark
From (1), $x = 1000 - y$ . Substituting in (2):
$10 (1000 - y) + 15 y = 12750$
$\Rightarrow 5 y = 2750 \Rightarrow y = 550$ , so $x = 450$
In June, 450 small and 550 large bottles were sold.
1 mark
(iii)(b) For July:
- $x + y = 2500$ ...(1)
- $12 x + 17 y = 34250$ ...(2)
1 mark
From (1), $x = 2500 - y$ . Substituting in (2):
$12 (2500 - y) + 17 y = 34250$
$\Rightarrow 5 y = 4250 \Rightarrow y = 850$ , so $x = 1650$
In July, 1650 small and 850 large bottles were sold.
1 mark

Answer: (i) 10x + 15y = 12750; (ii) 12x + 17y = 34250; (iii)(a) 450 small, 550 large; (iii)(b) 1650 small, 850 large

Where the marks are

(i) Forms 10x + 15y = 12750 (1 mark)
(ii) Forms 12x + 17y = 34250 (1 mark)
(iii)(a) Writes the pair x + y = 1000 and 10x + 15y = 12750 (1 mark)
(iii)(a) Solves to x = 450, y = 550 (1 mark)
(iii)(b) Writes the pair x + y = 2500 and 12x + 17y = 34250 (1 mark)
(iii)(b) Solves to x = 1650, y = 850 (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 paperSample paper 2026-27 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 36

Hints

Step-by-step solution

Revise the chapter

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