Question

A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
  (A)30
  (B)24
  (C)20
  (D)60

Answer 1

Hint- In order to solve this question first we will calculate the time interval of red light and green light for one minute, then by considering the common multiple of both red and green light we will proceed further to find the final answer.

Complete step-by-step solution -
Given statement: a red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals.
The red light will flash for the first time in one minute after $\dfrac{{60}}{3} = 20\sec $
That means it will flash at an interval of 20 sec each time \[ = 20sec,40sec,60sec,80sec,100sec,120sec\] and so on (multiples of 20)
Similarly the green light will flash for the first time in two minutes after $\dfrac{{120}}{5} = 24\sec $
That means it will flash at an interval of 24 sec each time \[ = 24sec,48sec,72sec,96sec,120sec,144sec\] and so on (multiples of 24)
Now take the common multiple of both red and green light which is =120
Which can also be done by simply taking the LCM of 20 and 24 = 120
Therefore both the lights will flash together for the first time in 120 sec
As we know
An hour has 3600 sec.
Therefore the number of intervals of 120 seconds in one hour is $\dfrac{{3600}}{{120}} = 30$
Hence, these two lights will flash together 30 times in each hour.
So, the correct answer is option A.

Note- In order to solve such types of problems where we need to find the happening of two different events with different time intervals at the same time, we take the LCM of both of the time as LCM is the first occurrence where both the events happen together.