Shortcut Trick
Checking for opposite directions, time = 200 ÷ (18 × 5/18) = 40 seconds (not given in options).
Thus, they are running in the same direction.
Relative speed = 10 − 8 = 2 km/h = 2 × (5/18) = 5/9 m/s.
Time to meet = Distance ÷ Relative speed = 200 ÷ (5/9) = 360 seconds.
Convert to minutes: 360 ÷ 60 = 6 minutes.
∴ The correct answer is 6 minutes.
Alternate Method
Given:
Length of circular path = 200 m
Speed of first child = 10 km/h
Speed of second child = 8 km/h
Formula Used:
Time taken to meet = Distance ÷ Relative Speed
Relative speed (same direction) = Speed1 − Speed2
Conversion from km/h to m/s = Multiply by 5/18
Calculations:
⇒ If they run in opposite directions, relative speed = 10 + 8 = 18 km/h = 18 × (5/18) = 5 m/s.
⇒ Time to meet = 200 ÷ 5 = 40 seconds (This is not among the given options).
⇒ Therefore, they must be running in the same direction.
⇒ Relative speed = 10 − 8 = 2 km/h
⇒ Relative speed in m/s = 2 × (5/18) = 5/9 m/s
⇒ Time taken to meet = Distance ÷ Relative speed = 200 ÷ (5/9)
⇒ Time = (200 × 9) ÷ 5 = 1800 ÷ 5 = 360 seconds
⇒ Converting seconds to minutes = 360 ÷ 60 = 6 minutes
∴ The correct answer is 6 minutes.
Additional Information
Meeting for the first time anywhere on the track
Time taken to meet for the first time = Length of track ÷ Relative speed.
Meeting for the first time at the starting point
Time taken = LCM of times taken by each individual to complete exactly one round independently.
Number of distinct meeting points
If the ratio of speeds is a : b (in simplest reduced form), the number of points is |a − b| for the same direction, and a + b for opposite directions.