Question : Racer A and Racer B run a race of 18 km on a circular track of length 800 m. Both complete one round in 200 seconds and 250 seconds, respectively. After how much time from the start will the faster person meet the slower person for the last time?
Option 1: 2700 seconds
Option 2: 4000 seconds
Option 3: 2250 seconds
Option 4: 1800 seconds
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Correct Answer: 4000 seconds
Solution : Given: Racer A and Racer B run a race of 18 km on a circular track of length 800 m. So, they will have to run = $\frac{18000}{800}=22.5$ rounds. Both complete one round in 200 seconds and 250 seconds, respectively. So, the speed of A = $\frac{800}{200}$ m/s = 4 m/s And, the speed of B = $\frac{800}{250}$ m/s = 3.2 m/s Racer A will complete the race in $200×22.5=4500$ seconds. So, the meeting time must be equal to or less than 4500 seconds. Time of meeting for the first time = $\frac{800}{4-3.2}$ m/s = 1000 seconds Since they meet every 1000 seconds and racer A will complete the race first in 4500 seconds, They will meet last at 4 × 1000 = 4000 seconds Hence, the correct answer is 4000 seconds.
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