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Half of the difference between… (Class 10 Maths 2023, Q26)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 26

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerPair of Linear Equations in Two Variables

Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Let the greater number be and the smaller be , then turn each sentence into an equation.

Hint 2

You should get and . Eliminate .

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 greater number be and the smaller number be .

    Half of their difference is 2:
    ...(i)

    1 mark

  2. The greater number plus twice the smaller number is 13:
    ...(ii)

    1 mark

  3. Subtract (i) from (ii): .

    Then .

    The numbers are 7 and 3.

    1 mark

Answer: 7 and 3

Where the marks are

  • Forms (1 mark)
  • Forms (1 mark)
  • Solves to get (1 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 paper2023 board paper, set 30/1/1 (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.