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

CBSE Class 10 Mathematics Standard 2026: question 33(A)

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, 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 answerQuadratic Equations

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

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

Hints

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

Hint 1

Let the faster train's speed be x km/h and write the slower one's speed in terms of x.

Hint 2

Time = distance ÷ speed. The slower train's time minus the faster train's time is 1 hour.

Hint 3

Clear the fractions to get a quadratic, factorise it, and reject the negative value.

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 of the faster train be $x$ km/h. Then the speed of the slower train is $(x - 10)$ km/h.
Time = distance/speed. The slower train takes 1 hour more for 200 km:
$\frac{200}{x - 10} - \frac{200}{x} = 1$
2 marks
Multiply both sides by $x (x - 10)$ :
$200 x - 200 (x - 10) = x (x - 10)$
$2000 = x^{2} - 10 x \Rightarrow x^{2} - 10 x - 2000 = 0$
1 mark
Factorise by splitting the middle term:
$x^{2} - 50 x + 40 x - 2000 = 0 \Rightarrow (x - 50) (x + 40) = 0$
1 mark
So $x = 50$ or $x = - 40$ . A speed cannot be negative, so we reject $x = - 40$ . Hence $x = 50$ .
½ mark
Speed of faster train = 50 km/h.
Speed of slower train = 50 − 10 = 40 km/h.
½ mark

Answer: Faster train: 50 km/h; slower train: 40 km/h

Where the marks are

Forms the equation $\frac{200}{x - 10} - \frac{200}{x} = 1$ (2 marks)
Reduces it to $x^{2} - 10 x - 2000 = 0$ (1 mark)
Factorises as $(x - 50) (x + 40) = 0$ (1 mark)
Rejects the negative root and takes x = 50 (½ mark)
States both speeds, 50 km/h and 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 paper2026 board paper, set 30/1/1 (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 33(A)

Hints

Step-by-step solution

Revise the chapter

More questions from Quadratic Equations