A and B run a 12 km race on a circular track of length 1200 m. They complete one round in 300 seconds and 400 seconds, respectively. After how much time from start will the faster person meet the slower person for the last time?

2400 seconds

length of race = 12 km = 12000 m

Length of 1 circular track = 1200 m

Number of rounds = \(\frac{12000}{1200}\) = 10

Time taken by A to complete one round = 300 seconds

Time taken by A to complete 10 rounds = 300 × 10 = 3000 seconds

Time taken by B to complete one round = 400 seconds

Time taken by B to complete 10 rounds = 400 × 10 = 4000 seconds

Both A and B started running ,

First meeting of A , B after 1200 sec ( LCM of 300 and 400 )

2nd meeting of A and B take place after = 2 × 1200 = 2400 sec

3rd meeting of A and B take place after = 3 × 1200 = 3600 sec

( It is not possible because A complete its 10 rounds in 3000 seconds )

Answer :- A will meet B last time after 2400 seconds.