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In a teachers' workshop, the… (Class 10 Maths 2024, Q27)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 27

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, 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-basedReal Numbers

In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

Fewest rooms means the largest group size that divides each subject count exactly.

Hint 2

Find the HCF of 48, 80 and 144, then divide each number by it.

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. To use the fewest rooms, each room must hold the largest possible equal number of teachers of one subject. That number is HCF(48, 80, 144).

    Prime factorise:

    ½ mark

  2. ½ mark

  3. ½ mark

  4. HCF, so 16 teachers sit in each room.

    ½ mark

  5. Minimum number of rooms .

    1 mark

Answer: 17 rooms

Where the marks are

  • Prime factorisation of 48 (½ mark)
  • Prime factorisation of 80 (½ mark)
  • Prime factorisation of 144 (½ mark)
  • HCF = 16 (½ mark)
  • Number of rooms = 3 + 5 + 9 = 17 (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 paper2024 board paper, set 30/1/1 (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.