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Sum of two numbers is 105 and… (Class 10 Maths 2024, Q22b)

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

CBSE Class 10 Mathematics Standard 2024: question 22(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerPair of Linear Equations in Two Variables

Sum of two numbers is 105 and their difference is 45. Find the numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Use two variables and write one equation for the sum and one for the difference.

Hint 2

Add the two equations.

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 numbers be and with . Then …(i).

    ½ mark

  2. Also …(ii).

    ½ mark

  3. Adding: , so , and then . The numbers are 75 and 30.

    1 mark

Answer: 75 and 30

Where the marks are

  • Forms (½ mark)
  • Forms (½ mark)
  • Solves to get 75 and 30 (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 paper2024 board paper, set 30/3/1 (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.