Traffic lights!

Number Theory Level pending

There are 4 traffic lights in a busy road. The traffic lights are such that, they change at equal intervals simultaneously, at 128 seconds, 40 seconds, 100 seconds, 50 seconds . All the three lights change simultaneously at 6:30 AM .

Then find the next time in which they will change lights simultaneously. Give your answer in decimal form, ignoring the seconds

For example, if your answer is

You have got that the light glow after 4 hour 3 minutes 4 seconds. Then your answer will be 10.3

The answer is 7.23.

1 solution

Viki Zeta
Jul 15, 2016

$\text{It's clearly given that the lights, switched at same time, and asked for } \\ \text{the next time it will change all-together same.}\\\text{So in this case LCM of it would give you the answer. To find LCM.} \\ 128 = 1 \times 2^7 \\ 100 = 1 \times 2^2 \times 5^2 \\ 50 = 1 \times 2 \times 5^2 \\ 40 = 1 \times 2^3 \times 5 \\ \therefore \text{ the LCM is } 2^7 \times 5^2 = 128 * 25 = 3200 \\ \text{So, the total no of seconds, after-which it will switch light simultaneously is 3200 seconds.} \\ \text{Now, we must convert it to minutes, 3200 seconds }\approx\text{ 53 minutes. } \\ \text{Therefore, when 53 minutes is passed by 6:30 AM, the time would be } 7:23\text{ Am.}\\\text{Therefore your answer will be } \fbox{7.23}$

Traffic lights!

The answer is 7.23.

1 solution

0 pending reports