Two persons started running on a circular track simultaneously with speeds of 20 m/s and 30 m/s in opposite directions. If the circumference of the circular track is 100 m, then find at how many distinct points they will cross each other?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 5.
We know that
Speed = Distance/Time taken
The time taken by the first person to complete a full lap is 100 m/20 m/s = 5 seconds
The time taken by the second person to complete a full lap is 100 m/30 m/s = 10/3 seconds
The LCM of 5 seconds and 10/3 seconds is 10 seconds, which means they will end up in the same initial positions after 10 seconds.
Let the two persons cross each other for the first time after x seconds.
Then, total distance covered by 1st person = 20x and the 2nd person = 30x
Now, the total distance covered by both the person = Circumference of the track
⇒ 30x + 20x = 100m
⇒ 50x = 100m
⇒ x = 2s
The two persons will cross each other for the first time after 2 seconds.
The two persons will cross each other again after 2 seconds, and then again after 2 seconds, and so on.
So in 10 seconds, they will meet = 10/2 = 5 times
Therefore the two persons will cross each other at 5 distinct points on the track