MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 34(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, 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 answerQuadratic Equations

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the same journey. Find the original speed of the train.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Time = distance ÷ speed; write the time taken at x km/h and at (x + 15) km/h.

Hint 2

Convert 30 minutes to hours and set the difference of the two times equal to it.

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/h. Time at original speed $= \frac{90}{x}$ h, at increased speed $= \frac{90}{x + 15}$ h. Difference is 30 min $= \frac{1}{2}$ h:
$\frac{90}{x} - \frac{90}{x + 15} = \frac{30}{60}$
2 marks
$\frac{90 ( x + 15 ) - 90 x}{x ( x + 15 )} = \frac{1}{2} \Rightarrow 2700 = x^{2} + 15 x \Rightarrow x^{2} + 15 x - 2700 = 0$
2 marks
$(x + 60) (x - 45) = 0 \Rightarrow x = 45$ or $x = - 60$ (rejected, speed cannot be negative). Original speed = 45 km/h.
1 mark

Answer: Original speed = 45 km/h

Where the marks are

Forms the time equation $\frac{90}{x} - \frac{90}{x + 15} = \frac{1}{2}$ (2 marks)
Reduces to $x^{2} + 15 x - 2700 = 0$ (2 marks)
Solves, rejects −60, speed 45 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 paper2026 board paper, set 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 34(b)

Hints

Step-by-step solution

Revise the chapter

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