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

CBSE Class 10 Mathematics Standard 2026: question 32

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section D, question 32, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32 · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream in 3 hours. Find the speed of the stream.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Upstream the stream slows the boat; downstream it helps. Write both speeds in terms of the stream's speed $x$ .

Hint 2

Total time = time upstream + time downstream = 3 hours.

Hint 3

Clear the fractions to get a quadratic and reject the value that is not physically possible.

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 stream be $x$ km/h. Upstream speed $= (12 - x)$ km/h, downstream speed $= (12 + x)$ km/h. Time = distance ÷ speed, so
$\frac{15}{12 - x} + \frac{18}{12 + x} = 3$
2 marks
$15 (12 + x) + 18 (12 - x) = 3 (144 - x^{2}) \Rightarrow 396 - 3 x = 432 - 3 x^{2} \Rightarrow 3 x^{2} - 3 x - 36 = 0 \Rightarrow x^{2} - x - 12 = 0$
1 mark
$x^{2} - 4 x + 3 x - 12 = 0 \Rightarrow (x - 4) (x + 3) = 0 \Rightarrow x = 4$ or $x = - 3$
1 mark
Speed cannot be negative, so $x = - 3$ is rejected. Hence the speed of the stream is 4 km/h.
1 mark

Answer: Speed of the stream = 4 km/h

Where the marks are

Forms the equation $\frac{15}{12 - x} + \frac{18}{12 + x} = 3$ (2 marks)
Reduces to $x^{2} - x - 12 = 0$ (1 mark)
Factorises to get $x = 4, - 3$ (1 mark)
Rejects $- 3$ ; speed = 4 km/h (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/5/1 (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 32

Hints

Step-by-step solution

Revise the chapter

More questions from Pair of Linear Equations in Two Variables