A b and c are moving on a circular track a who is the only one moving in anticlockwise direction and moves at a speed of twice that of b and thrice that of c takes 10 sec to cover the entire track if all the three start simultaneously when they meet for the second time after the start
Answers
Answer:
The time taken by Rakesh to complete one round =circular races 01=140 sec
Similarly, the time taken by Brijesh to complete one round = 60 sec
Observe that Rakesh and Brijesh will keep on coming to the starting point after every multiple of 140 and 60 respectively.
So, the time taken by them to meet at the starting point must be divisible by both 140 and 60, i.e., LCM of (140 and 60) = 420sec.
Hence they will meet at the starting point after 420 seconds from the start, which is nothing but the LCM of respective time taken by both to complete their one round.
Now, let’s take question (b), i.e., first meeting point anywhere on the track.
For this, we will use a simple approach.
The ratio of the speed of Brijesh and speed of Rakesh = 7:3.
As they are moving in the same direction, the relative speed is 7 – 3 = 4 m/s.
Also note that when they meet at the starting point, they take 420 seconds. In this time they cover 7 and 4 rounds respectively. (Brijesh covers one round in 60 seconds so, in 210 seconds he will cover 420/60 = 7 rounds. Similarly, Rakesh will cover 3 rounds).
That makes complete sense because when the time is constant, the distance covered is directly proportional to the speed and hence, the ratio of the distance covered by two bodies is equal to the ratio of their speeds.
Coming back to the question, we observe that, when they meet again at the starting point, Brijesh completes 4 more rounds (which is numerically equal to their relative speed) than Rakesh does. Also, they will meet for the first time when Brijesh would have taken a lead of one round over Rakesh.
That means, when they meet at the starting point, it would be their fourth meeting.
And it took 420 seconds as calculated above. Therefore, time taken to meet for the first time = 420/4 = 105 seconds.
We can also find the exact point of their first meeting on the track by finding the distance traveled by Rakesh in 105 seconds with the speed of 3m/s, i.e., 105×3 = 315 meters away from the starting point in the direction of their motion.