Question

The traffic lights at three different road crossings change after
every 48 seconds, 72 seconds and 108 seconds respectively. If
the change simultaneously at 8 a.m at what time time will they
change simultaneously again?​

Answer 1

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Required Answer:-

If the traffic lights change simultaneously at 8 a.m, then they will change simultaneously again after the LCM of the duration i.e. 48 s, 72 s and 108 s.

Then, finding the LCM of these durations by prime factorisation

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

LCM is the product of highest degrees of factors. Then, LCM of 48, 72 and 108 is 2⁴ × 3³ = 432 seconds.

Hence:-

They will change after 432 seconds i.e. 7 minutes 12 seconds. The traffic lights will change after:

➙ 8 am + 7 minutes 12 seconds

➙ 08 : 07 : 12 am. (Answer)

Answer 2

Answer:

Ncert solutions

Grade 6

Mathematics

Chapters in NCERT Solutions - Mathematics, Class 6

Exercises in Playing With Numbers

Question 1

Q6) 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 simultaneously again?

SOLUTION:

to find the at what time the lights will change simultaneously we need to find the LCM of 48, 72 and 108

LCM of 42, 72 and 108

=2\times2\times3\times3\times2\times2\times3=2×2×3×3×2×2×3

432\div60\min\ =\ 7\min\ 12\ \sec432÷60min = 7min 12 sec

hence, the lights will again change simultaneously at 7mins 12sec past 7 am.