Question : 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 the start will the faster person meet the slower person for the last time?
Option 1: 2400 Seconds
Option 2: 8400 seconds
Option 3: 9600 seconds
Option 4: 10800 seconds
Correct Answer: 2400 Seconds
Solution :
The total distance of the race is 12 km, and the length of the track is 1200 m (or 1.2 km).
So, the number of rounds to complete the race = $\frac{12}{1.2}$ = 10 rounds
Now, let's find out when A and B will meet for the first time.
They will meet when A completes one more round than B.
The least common multiple of 300 and 400 is 1200.
So, A and B will meet every 1200 seconds.
The time it takes for A to complete the race = 10 × 300 = 3000 seconds.
So, the number of meetings = $\frac{3000}{1200}$ = 2.5
Since they can't meet half a time, we round this down to 2.
Therefore, they will meet for the last time at 2 × 1200 = 2400 seconds from the start.
Hence, the correct answer is 2400 seconds.
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