Skip to content

The monthly income of… (Class 10 Maths SQP 2025-26, Q31A)

questionbuddy.in/q/cbse-10-maths-2025-26-sqp-standard-q31a-monthly-income-aryan-babban-ratio

MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 31(A)

From the official CBSE sample question paper for 2025-26, section C, question 31(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(A) · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

The monthly income of Aryan and Babban are in the ratio 3:4 and their monthly expenditures are in ratio 5:7. If each saves ₹ 15,000 per month, find their monthly incomes.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Use one variable for the income ratio and another for the expenditure ratio.

Hint 2

Savings = income − expenditure gives you two equations.

Hint 3

Solve by elimination and multiply x by 3 and by 4.

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 of Aryan and Babban be ₹ and ₹, and their expenditures be ₹ and ₹.

    1 mark

  2. Savings = income − expenditure, so
    … (1)
    … (2)

    1 mark

  3. (1)×4: . (2)×3: . Subtracting gives . Then , so .
    Monthly incomes: Aryan ₹ = ₹90,000 and Babban ₹ = ₹1,20,000.

    1 mark

Answer: Aryan ₹90,000; Babban ₹1,20,000

Where the marks are

  • Takes incomes as 3x, 4x and expenditures as 5y, 7y (1 mark)
  • Forms the equations and (1 mark)
  • Solves to x = 30000 and gives the incomes ₹90,000 and ₹1,20,000 (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 paperSample paper 2025-26 (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.