Question

1) A mtro train on platform A arrives after every 3 minutes 12 seconds and another metro train on platform B arrvies after every 1 mintues 12 seconds. At 8 am on a particular day both trains arrive on the respective platforms together. At what time will both the platforms have trians together again ?

Please show with the workings

Answer 1

Train A reaches at every 3 mins 12 seconds=192seconds

Train B reaches at every 1min 12 seconds=72 seconds.

Now, both trains should reach at same time.
This happens at LCM of 192 and 72.
So, Let us find LCM of 192 and 72.
ind the prime factorization of 192
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
Find the prime factorization of 72
72 = 2 × 2 × 2 × 3 × 3
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
LCM = 576
So, LCM is 576.
So, both trains arrive at 576 seconds after 8.00 am. 576 s = 9 mins 36 seconds.

So, trains come together after 9 mins, 36 seconds after 8.00 am.