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The traffic lights at three… (Class 10 Maths 2023, Q26b)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 26(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerCompetency-basedReal Numbers

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

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 common multiple of all three intervals; you want the smallest such.

Hint 2

Find the LCM by prime factorisation, then convert seconds into minutes and seconds.

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. The lights change together after a time that is the LCM of 48, 72 and 108 seconds.
    , ,

    1 mark

  2. LCM seconds.

    1 mark

  3. s min min s. So the lights will next change together at 7 : 07 : 12 a.m. (7 minutes 12 seconds past 7 a.m.).

    1 mark

Answer: LCM = 432 s = 7 min 12 s; next simultaneous change at 7:07:12 a.m.

Where the marks are

  • Prime factorises 48, 72 and 108 (1 mark)
  • Finds LCM = 432 seconds (1 mark)
  • Converts to 7 min 12 s and states the time 7:07:12 a.m. (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 paper2023 board paper, set 30/5/1 (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.