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The sum of two numbers… (Class 10 Maths SQP 2025-26, Q10)

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MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 10

From the official CBSE sample question paper for 2025-26, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQReal Numbers

The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such numbers are

  1. (A)2
  2. (B)3
  3. (C)4
  4. (D)5

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

Write each number as 81 times something.

Hint 2

The two multipliers must be co-prime, otherwise the HCF would be larger than 81.

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. Since the HCF is 81, write the numbers as and , where and are co-prime. Then , so .

  2. The co-prime pairs with sum 15 are (1,14), (2,13), (4,11) and (7,8). The pairs (3,12), (5,10) and (6,9) are rejected because they share a common factor. So there are 4 pairs, which is option (C).

    1 mark

Answer: 4 pairs, option (C)

Where the marks are

  • Reduces to with x, y co-prime and counts 4 pairs, option (C) (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, 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.