MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section D, question 34(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(b) · 5 marks · Long answerCompetency-basedQuadratic Equations

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.

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

Hints

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

Hint 1

Write the time taken at the original speed and at the reduced speed, using time = distance ÷ speed.

Hint 2

The difference between the two times is 3 hours. Form the equation and clear the fractions.

Hint 3

You get $x^{2} - 8 x - 1280 = 0$ . Find two factors of 1280 that differ by 8, and remember that speed cannot be negative.

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 reduced speed is $(x - 8)$ km/h.
½ mark
Time $= \frac{distance}{speed}$ . The slower journey takes 3 hours more, so
$\frac{480}{x - 8} - \frac{480}{x} = 3.$
1½ marks
Take the LCM: $480 [\frac{x - ( x - 8 )}{x ( x - 8 )}] = 3$ .
So $\frac{3840}{x ( x - 8 )} = 3$ , which gives $x (x - 8) = 1280$ .
Hence $x^{2} - 8 x - 1280 = 0$ .
1 mark
Factorise: $x^{2} - 40 x + 32 x - 1280 = 0$ , so $(x - 40) (x + 32) = 0$ .
Therefore $x = 40$ or $x = - 32$ .
1 mark
Speed cannot be negative, so we reject $x = - 32$ .
The speed of the train is 40 km/h.
Check: $480/40 = 12$ h and $480/32 = 15$ h, a difference of 3 h.
1 mark

Answer: Speed of the train = 40 km/h.

Where the marks are

Takes the speed as $x$ and the reduced speed as $x - 8$ (½ mark)
Forms the equation $\frac{480}{x - 8} - \frac{480}{x} = 3$ (1½ marks)
Simplifies to $x^{2} - 8 x - 1280 = 0$ (1 mark)
Factorises to get $x = 40$ or $- 32$ (1 mark)
Rejects the negative root and states the speed as 40 km/h (1 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 paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 34(b)

Hints

Step-by-step solution

Revise the chapter

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