Question : In a circular race of 1600 m, A and B start from the same point and at the same time at speeds of 27 km/hr and 45 km/hr, respectively. After how long will they meet again for the first time on the racetrack, when they are running in the same direction?
Option 1: 90 seconds
Option 2: 320 seconds
Option 3: 240 seconds
Option 4: 180 seconds
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Correct Answer: 320 seconds
Solution : Given: Length of the track = 1600 m The relative speed of A and B with both going in the same direction is 45 – 27 = 18 km/hr ⇒ $18 \times \frac{5}{18} = 5$ $\text{m/s}$ The time they meet again on the track for the first time when they are both running in the same direction $=\frac{\text{Length of the track}}{\text{The relative speed of A with B in the same direction}}=\frac{1600}{5} = 320$ $\text{seconds}$ Hence, the correct answer is 320 seconds.
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