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The monthly incomes of two… (Class 10 Maths 2025, Q27)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 27

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

The monthly incomes of two persons are in the ratio 9 : 7 and their monthly expenditures are in the ratio 4 : 3. If each saved ₹ 5,000, express the given situation algebraically as a system of linear equations in two variables. Hence, find their respective monthly incomes.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

Use for incomes and for expenditures.

Hint 2

Savings = income − expenditure gives two equations; 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 incomes be ₹ and ₹ and expenditures ₹ and ₹. Saving = income − expenditure:
    ...(i)

    1 mark

  2. ...(ii)

    1 mark

  3. (i)×3: ; (ii)×4: . Subtracting: (and ).

    ½ mark

  4. Monthly incomes: ₹45000 and ₹35000.

    ½ mark

Answer: ₹45,000 and ₹35,000

Where the marks are

  • Forms (1 mark)
  • Forms (1 mark)
  • Solves to get (½ mark)
  • States incomes ₹45000 and ₹35000 (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 paper2025 board paper, set 30/4/1 (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.