MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 31

From the official CBSE sample question paper for 2024-25, 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 a two-digit number and the number obtained by reversing the order of its digits is 99. If ten's digit is 3 more than the unit's digit, then find the number.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

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

Hint 2

Form two equations, one from each condition, and solve them together.

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 ten's digit be $x$ and the unit's digit be $y$ . Then the number is $10 x + y$ .
½ mark
The reversed number is $10 y + x$ , so $(10 x + y) + (10 y + x) = 99$ .
½ mark
$11 x + 11 y = 99 \Rightarrow x + y = 9$ …(i)
½ mark
The ten's digit is 3 more than the unit's digit: $x = y + 3$ …(ii)
½ mark
Substituting (ii) in (i): $2 y + 3 = 9 \Rightarrow y = 3$ , so $x = 6$ .
½ mark
The required number is $10 (6) + 3 = 63$ .
½ mark

Answer: 63

Where the marks are

Represents the number as $10 x + y$ (½ mark)
Forms the equation for number + reversed number = 99 (½ mark)
Simplifies to $x + y = 9$ (½ mark)
Writes $x = y + 3$ (½ mark)
Solves to get $x = 6$ , $y = 3$ (½ mark)
States the number 63 (½ mark)

Revise the chapter

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

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 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 31

Hints

Step-by-step solution

Revise the chapter

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