Question

9. The traffic lights at four different road crossings change after every 24 seconds,
48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at
8 a.m., at what time will they change simultaneously again?​

Answer 1

Answer:

• The traffic lights will change simultaneously again at 8:07:12 a.m.

Step-by-step explanation:

Given that:

• The traffic lights at four different road crossings change after every 24 seconds, 48 seconds, 72 seconds and 108 seconds.
• They change simultaneously at 8 a.m.

To Find:

• At what time will they change simultaneously again?

Solution:

Time after which the lights will change simultaneously again = LCM of 24, 48, 72 and 108

Calculating LCM of 24, 48, 72 and 108:

$\Large{\begin{array}{c|c}\underline{2}&\underline{24,48,72,108}\\\underline{2}&\underline{\;12,24,36,54\;}\\\underline{2}&\underline{\;\;6,12,18,27\;\;}\\\underline{3}&\underline{\;\;\;\;3,6,9,27\;\;\;\;}\\\underline{3}&\underline{\;\;\;\;\;1,2,3,9\;\;\;\;\;}\\&1,2,1,3\end{array}}$

Hence,

The traffic lights will change simultaneously again after:

$\sf{\longmapsto (2\times2\times2\times3\times3\times2\times3)\;seconds}$

Multiplying the numbers,

$\sf{\longmapsto 432\;seconds}$

Converting 432 seconds into minute:

As we know that,

• 1 minute = 60 seconds

Therefore,

432 seconds = 420 seconds + 12 seconds = 7 minute + 12 seconds

Hence,

• 432 seconds = 7 minutes and 12 seconds

Finding time at which the lights will change simultaneously again:

As it is given:

• The lights changed simultaneously at 8 a.m.

Time at which the lights will change simultaneously again:

$\sf{\longmapsto8\;am+7\;minutes+12\;seconds }$

$\bf{\longmapsto8:07:12\;am}$