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Find the length of the plank… (Class 10 Maths 2026, Q21)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 21

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerReal Numbers

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Least time means the longest plank that measures both lengths exactly.

Hint 2

Change both lengths to cm and find their HCF by prime factorisation.

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. Convert to the same unit: 4 m 20 cm cm and 5 m 4 cm cm.

    ½ mark

  2. To measure in the least time, the plank must be as long as possible while dividing both lengths exactly. So we need HCF(420, 504).

    and .

    1 mark

  3. HCF . The required length of the plank is 84 cm.

    ½ mark

Answer: 84 cm

Where the marks are

  • Converts both lengths to cm: 420 cm and 504 cm (½ mark)
  • Writes the prime factorisations of 420 and 504 (1 mark)
  • Gets HCF = 84 cm (½ 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 paper2026 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.