In a circular race of 750 m, X and Y start from the same point and at the same time with speeds of 9 km/h and 13.5 km/h, respectively. If they are running in the same direction, after how many seconds will they meet again for the first time on the track?

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Let's convert the speeds from km/h to m/s:

Speed of X = 9 km/h = (9 × 1000) / 3600 = 2.5 m/s
Speed of Y = 13.5 km/h = (13.5 × 1000) / 3600 = 3.75 m/s

Since they are running in the same direction, their relative speed = 3.75 m/s - 2.5 m/s = 1.25 m/s.

They will meet again for the first time when the faster runner (Y) has gained one full lap (750 m) over the slower runner (X).

Time taken = Distance to be gained / Relative speed = 750 m / 1.25 m/s = 600 seconds.

Therefore, they will meet again for the first time after 600 seconds.

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