MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section D, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerCompetency-basedQuadratic Equations

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered 2 m extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Let the original length be x m and write price per metre before and after the offer.

Hint 2

The price per metre drops by ₹120: subtract the two expressions and equate to 120.

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 the original length be $x$ m. Original price per metre $= ₹ \frac{2100}{x}$ ; with 2 m extra, price per metre $= ₹ \frac{2100}{x + 2}$ . Given: $\frac{2100}{x} - \frac{2100}{x + 2} = 120$ .
2 marks
$\frac{2100 \times 2}{x ( x + 2 )} = 120 \Rightarrow x (x + 2) = 35 \Rightarrow x^{2} + 2 x - 35 = 0$ .
1 mark
$x^{2} + 7 x - 5 x - 35 = 0 \Rightarrow (x + 7) (x - 5) = 0 \Rightarrow x = - 7$ or $x = 5$ .
1 mark
Length cannot be negative, so $x = 5$ .
½ mark
Original length = 5 m and original price per metre $= \frac{2100}{5} = ₹420$ .
½ mark

Answer: Original price = ₹420 per metre; original length = 5 m

Where the marks are

Forms $\frac{2100}{x} - \frac{2100}{x + 2} = 120$ (2 marks)
Reduces to $x^{2} + 2 x - 35 = 0$ (1 mark)
Factorises to $(x + 7) (x - 5) = 0$ (1 mark)
Rejects negative root, $x = 5$ (½ mark)
States price ₹420 per metre (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Quadratic Equations

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/4/1 (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 2026: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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