MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 31

From the official CBSE sample question paper for 2026-27, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerPair of Linear Equations in Two Variables

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

A two-digit number with tens digit $x$ and units digit $y$ equals $10 x + y$ .

Hint 2

Write two equations from the two conditions and solve them by substitution.

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 tens digit be $x$ and the units digit be $y$ . Then the number is $10 x + y$ and the reversed number is $10 y + x$ .
½ mark
$x + y = 9$ ...(1)
½ mark
$9 (10 x + y) = 2 (10 y + x) \Rightarrow 90 x + 9 y = 20 y + 2 x \Rightarrow 88 x = 11 y \Rightarrow y = 8 x$ ...(2)
½ mark
Substituting (2) in (1): $x + 8 x = 9 \Rightarrow x = 1$ , so $y = 8$
1 mark
Required number $= 10 (1) + 8 = 18$
½ mark

Answer: 18

Where the marks are

Expresses the number and its reverse in terms of the digits (½ mark)
Forms x + y = 9 (½ mark)
Forms 9(10x + y) = 2(10y + x) (½ mark)
Solves to get x = 1, y = 8 (1 mark)
Number = 18 (½ 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 paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 31

Hints

Step-by-step solution

Revise the chapter

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