MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 33(B)

From the official CBSE sample question paper for 2025-26, section D, question 33(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(B) · 5 marks · Long answerQuadratic Equations

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hr, it takes 2 hours less in the journey. Find the original speed of the train.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Time = Distance ÷ Speed; write the time for both speeds in terms of $x$ .

Hint 2

The difference between the two times is 2 hours; form the equation and simplify to a quadratic.

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 speed be $x$ km/hr. Time taken $= \frac{300}{x}$ hr.
½ mark
New speed $= (x + 5)$ km/hr; new time $= \frac{300}{x + 5}$ hr.
½ mark
Given: $\frac{300}{x} - \frac{300}{x + 5} = 2$
1 mark
$\frac{300 ( x + 5 ) - 300 x}{x ( x + 5 )} = 2 \Rightarrow \frac{1500}{x ^{2} + 5 x} = 2 \Rightarrow x^{2} + 5 x - 750 = 0$
1½ marks
$x^{2} + 30 x - 25 x - 750 = 0 \Rightarrow (x + 30) (x - 25) = 0 \Rightarrow x = 25$ or $x = - 30$
1 mark
Speed cannot be negative, so $x = 25$ . The original speed of the train is 25 km/hr.
½ mark

Answer: 25 km/hr

Where the marks are

Original time $\frac{300}{x}$ (½ mark)
New time $\frac{300}{x + 5}$ (½ mark)
Forms equation $\frac{300}{x} - \frac{300}{x + 5} = 2$ (1 mark)
Reduces to $x^{2} + 5 x - 750 = 0$ (1½ marks)
Factorises to get $x = 25$ or $- 30$ (1 mark)
Rejects $- 30$ , speed 25 km/hr (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 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 33(B)

Hints

Step-by-step solution

Revise the chapter

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