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National Art convention… (Class 10 Maths SQP 2023-24, Q26)

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MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 26

From the official CBSE sample question paper for 2023-24, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerCompetency-basedReal Numbers

National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Equal-sized groups with the fewest groups means the largest possible group size.

Hint 2

Find the HCF of 60, 84 and 108, 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. Every group must have the same number of students, and the number of groups must be as small as possible. So the group size must be the largest number that divides 60, 84 and 108, that is, HCF(60, 84, 108).

    ½ mark

  2. Prime factorisation: , , .

    So HCF , and each group has 12 students.

    ½ mark

  3. Number of groups in music

    ½ mark

  4. Number of groups in dance

    ½ mark

  5. Number of groups in handicrafts

    ½ mark

  6. Each group gets one room. Total rooms required .

    ½ mark

Answer: 12 students per group; Music 5, Dance 7, Handicrafts 9 groups; 21 rooms

Where the marks are

  • Recognises that the group size is HCF(60, 84, 108) (1/2 mark)
  • Finds HCF = 12 (1/2 mark)
  • Music groups = 5 (1/2 mark)
  • Dance groups = 7 (1/2 mark)
  • Handicraft groups = 9 (1/2 mark)
  • Total rooms = 21 (1/2 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 2023-24 (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.