MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 33(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, 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 answerCompetency-basedQuadratic Equations

The time taken by a person to travel an upward distance of 150 km was $2 \frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of 10 km/h more than the speed while going up, find the speeds in each direction.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Let the upward speed be $x$ km/h. What is the downward speed then?

Hint 2

Write each time as distance ÷ speed. The upward time minus the downward time equals $\frac{5}{2}$ hours.

Hint 3

Clear the fractions to get a quadratic in $x$ , then factorise and 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 speed while going up be $x$ km/h. Then the speed on the downward return journey is $(x + 10)$ km/h.
½ mark
Time = $\frac{distance}{speed}$ .
Time going up $= \frac{150}{x}$ h and time coming down $= \frac{150}{x + 10}$ h.
The upward trip takes $2 \frac{1}{2} = \frac{5}{2}$ h more:
$\frac{150}{x} - \frac{150}{x + 10} = \frac{5}{2}$
2 marks
$\frac{150 ( x + 10 ) - 150 x}{x ( x + 10 )} = \frac{5}{2} \Rightarrow \frac{1500}{x ^{2} + 10 x} = \frac{5}{2}$
$\Rightarrow 5 (x^{2} + 10 x) = 3000 \Rightarrow x^{2} + 10 x - 600 = 0$
1 mark
Factorise: $x^{2} + 30 x - 20 x - 600 = 0 \Rightarrow (x + 30) (x - 20) = 0$
½ mark
So $x = - 30$ or $x = 20$ . Speed cannot be negative, so $x = 20$ .
½ mark
Downward speed $= x + 10 = 30$ km/h.
Check: $\frac{150}{20} - \frac{150}{30} = 7.5 - 5 = 2.5$ h ✓
Speed going up = 20 km/h; speed coming down = 30 km/h.
½ mark

Answer: Upward speed 20 km/h, downward speed 30 km/h

Where the marks are

Takes the upward speed as $x$ and the downward speed as $x + 10$ (½ mark)
Forms the equation $\frac{150}{x} - \frac{150}{x + 10} = \frac{5}{2}$ (2 marks)
Simplifies it to $x^{2} + 10 x - 600 = 0$ (1 mark)
Factorises it as $(x + 30) (x - 20) = 0$ (½ mark)
Gets $x = 20$ , rejecting the negative root (½ mark)
Gets the downward speed of 30 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 paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 33(b)

Hints

Step-by-step solution

Revise the chapter

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