Question

A red-light flashes 3 times per minute, green light flashes 4 times per minute and yellow light flashes 6 times per minute at regular intervals. If all three lights start flashing at the same time, how many times do they flash together in each 75 minutes?

Answer 1

Hint: In such a type of question write down a sequence of time at which each light flashes out. Then write common time at which they flash out simultaneously. After that count the number of times they all flash out simultaneously within the given time period.

Complete step-by-step answer:
The following information can be written from the given question.
Time interval for red light to flash $3\text{ times per minute}$
Time interval for green light to flash $\text{4 times per minute}$
Time interval for yellow light to flash $\text{6 times per minute}$
Now if we want to find out the time at which all light flashes simultaneously, we have to find out the common multiple of flashing time of red green and yellow light.
Now red light flashes out at the multiple of 3 minutes so flashing time of red light are
$3,6,9,12,15,18,21,24,.....----(a)$
Similarly, we can write green light flashes out at the multiple of 4 minutes so flashing time of green light are
$4,8,12,16,24,28......-----(b)$
Similarly, we can write yellow light flashes out at the multiple of 6 minutes so flashing time of yellow light are
$6,12,18,24,30.......----(c)$
So, we get three sequence of flashing of red, green and yellow light respectively
Hence, we see that all light flashes out simultaneously at time interval of(in minutes)
$12,24,36,....---(d)$
Now we have to find out number of times all flashes out simultaneously in 75 minutes
So, all light flashes out at following minutes
$12,24,36,48,60,72$
Hence, all light flashes simultaneously 6 times.

NOTE: In order to find out such a type of question, find the LCM of flashing time of different light. This LCM is the time after which they flash out simultaneously for the first time. Now find the greatest integer of $\left[ \dfrac{75}{LCM} \right]$ . This gives the number of times that all light flashes simultaneously in 75 minutes.