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The ratio of monthly… (Class 10 Maths Basic 2024, Q33)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 33

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section D, question 33, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

The ratio of monthly incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save ₹ 2,000 per month, then find their monthly incomes.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Use two different variables for the income ratio and the expenditure ratio.

Hint 2

Income − expenditure = saving gives two linear 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 monthly incomes be ₹ and ₹, and the expenditures be ₹ and ₹.

    1 mark

  2. Saving = income − expenditure, so for the first person: ...(i)

    1 mark

  3. For the second person: ...(ii)

    1 mark

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

    1 mark

  5. Monthly incomes: and .

    1 mark

Answer: ₹18,000 and ₹14,000

Where the marks are

  • Takes incomes 9x, 7x and expenditures 4y, 3y (1 mark)
  • Forms (1 mark)
  • Forms (1 mark)
  • Solves to get (1 mark)
  • States incomes ₹18000 and ₹14000 (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 430/5/1 (Basic): 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.