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In a 2-digit number, the digit… (Class 10 Maths 2024, Q31)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 31

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, 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

In a 2-digit number, the digit at the unit's place is less than the digit at the ten's place. The product of the digits is . Find the number.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Let the ten's digit be and express the unit's digit in terms of .

Hint 2

Form a quadratic from the product of the digits and factorise 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.

  1. Let the ten's digit be ; then the unit's digit is .

    ½ mark

  2. Product of digits:

    ½ mark

  3. ½ mark

  4. ½ mark

  5. or ; a digit cannot be negative, so and unit's digit .

    ½ mark

  6. Required number .

    ½ mark

Answer: 94

Where the marks are

  • Unit's digit (½ mark)
  • Equation (½ mark)
  • Quadratic (½ mark)
  • Factorisation (½ mark)
  • Rejects , (½ mark)
  • Number 94 (½ mark)

Revise the chapter

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 paper2024 board paper, set 30/2/1 (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.