Question

A red light flashes 3 times per minute, green light flashes 4 times per minute and yellow light flashes 6 times a minute at regular intervals. If all the three lights flash at the same time, how many times do they flash in 75 minutes?
\[\begin{align}
  & \text{A}\text{. 60} \\
 & \text{B}\text{. 65} \\
 & \text{C}\text{. 70} \\
 & \text{D}\text{. 75} \\
\end{align}\]

Answer 1

Hint: It is clear that a red light flashes 3 times per minute, green light flashes 4 times per minute and yellow light flashes 6 times a minute at regular intervals. Now, we should find the time interval that all the three lights flash at a time. We know that 1 minute has 60 seconds. Now we should calculate the time taken by each light to flash once. Now we should find the L.C.M of all the time intervals taken by a flashlight to flash once. This will give us the time required for all the three flash lights to flash at once. Now we should find the time required by the three flash lights to flash at a time in a duration of 75 minutes.

Complete step-by-step answer:
From the question, it is clear that a red light flashes 3 times per minute, green light flashes 4 times per minute and yellow light flashes 6 times a minute at regular intervals. Now, we should find the time interval that all the three lights flash at a time.

We know that 1 minute has 60 seconds. Now we should calculate the time taken by each light to flash once. Then, we get
The time taken by red light to flash once \[\text{=}\dfrac{60}{3}s=20s\]
The time taken by green light to flash once \[\text{=}\dfrac{60}{4}s=15s\]
The time taken by yellow light to flash once \[\text{=}\dfrac{60}{6}s=10s\]
So, it is clear we should find the time where the three lights flash at a time. So, now we should find the time which is a least common multiple of 10, 15 and 20.
Multiples of 10 \[=10,20,30,40,50,60,70,80,90,....\]
Multiples of 15 \[=15,30,45,60,75,90,105,120,135,....\]
Multiples of 20 \[=20,40,60,80,100,120,140,160,180,....\]
From the multiples of 10, 15 and 20, the least common multiple is 60. So, we can say that the three flash lights flash every 60 seconds. We know that 1 minute is equal to 60 seconds.
So, it is clear that the three lights flash at a time every minute.
From the question, it is clear that they find the time taken by three flashes of time in 75 minutes. Let us assume this time is equal to t.
\[\begin{align}
  & 1\to 1 \\
 & 75\to x \\
\end{align}\]
By cross multiplication, we get
\[\begin{align}
  & \Rightarrow (1)(x)=(1)(75) \\
 & \Rightarrow x=75....(1) \\
\end{align}\]
From equation (1), it is clear that the three lights flash at a time 75 times in 75 minutes.

So, the correct answer is “Option D”.

Note: Students should make calculations in a correct manner. If a small mistake is done, then the final answer may get interrupted. So, there should be no mistake in calculation. While solving this problem, students should be able to understand the given data in a correct manner. Based on the observation, the student can solve the problem. So, students should have a clear view on the problem.