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The traffic lights at… (Class 10 Maths Basic 2025, Q29)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 29

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCompetency-basedReal Numbers

The traffic lights at three different road crossings change after every 45 seconds, 75 seconds and 60 seconds respectively. If they change together at 5.00 a.m., then at what time they will change together next?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

The lights change together again after a time that is a multiple of 45, 75 and 60 at once.

Hint 2

Find the LCM using prime factorisation, convert seconds to minutes and add to 5:00 a.m.

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. Prime factorisation: , ,

    1½ marks

  2. LCM

    ½ mark

  3. 900 seconds minutes

    ½ mark

  4. The lights will next change together 15 minutes after 5:00 a.m., i.e. at 5:15 a.m.

    ½ mark

Answer: 5:15 a.m.

Where the marks are

  • Correct prime factorisation of 45, 75, 60 (1½ marks)
  • LCM = 900 (½ mark)
  • Converts 900 s to 15 minutes (½ mark)
  • Next change together at 5:15 a.m. (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 paper2025 board paper, set 430/5/1 (Basic): 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.