MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 33(A)

From the official CBSE sample question paper for 2026-27, section D, question 33(A), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(A) · 5 marks · Long answerCompetency-basedQuadratic Equations

A train travels a distance of 360 km at a uniform speed. If the speed had been 5 km/h more, then it would have taken 1 hour less to cover the same distance. Find the speed of the train.

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

Write the time taken at speed $x$ and at speed $x + 5$ ; their difference is 1 hour.

Hint 2

Clear the denominators to get a quadratic, then reject the negative root.

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 uniform speed of the train be $x$ km/h; the increased speed is $(x + 5)$ km/h.
½ mark
Time = distance ÷ speed, so $\frac{360}{x} - \frac{360}{x + 5} = 1$
1 mark
$360 (x + 5) - 360 x = x (x + 5) \Rightarrow 1800 = x^{2} + 5 x \Rightarrow x^{2} + 5 x - 1800 = 0$
1 mark
$x = \frac{- 5 \pm 25 + 7200}{2} = \frac{- 5 \pm 85}{2}$
1 mark
$x = 40$ or $x = - 45$
1 mark
Speed cannot be negative, so $x = 40$ . The speed of the train is 40 km/h.
½ mark

Answer: 40 km/h

Where the marks are

Defines the speed variable (½ mark)
Forms the time equation (1 mark)
Simplifies to $x^{2} + 5 x - 1800 = 0$ (1 mark)
Applies the quadratic formula or factorisation (1 mark)
Gets roots 40 and −45 (1 mark)
Rejects the negative root; speed = 40 km/h (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 33(A)

Hints

Step-by-step solution

Revise the chapter

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