There are 8 equidistant points A, B, C, D, E, F, G and H in the clockwise direction on the periphery of a circle. In a time interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start, will the two persons meet each other ?

There are 8 equidistant points A, B, C, D, E, F, G and H in the clockwise direction on the periphery of a circle. In a time interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start, will the two persons meet each other ? Correct Answer 7t

Distance covered by first person in time t = $$\frac{2}{8}$$ round = $$\frac{1}{4}$$ round
Distance covered by second person in time t = $$\frac{3}{8}$$ round
Speed of the first person = $$\frac{1}{4t}$$
Speed of the second person = $$\frac{3}{8t}$$
Since the two persons start from A and B respectively, so they shall meet each other when there is a difference of $$\frac{7}{8}$$ round between the two.
Relative speed of A and B :
$$\eqalign{ & = \left( {\frac{3}{{8t}} - \frac{1}{{4t}}} \right) \cr & = \frac{1}{{8t}} \cr} $$
Time taken to cover $$\frac{7}{8}$$ round at this speed :
$$\eqalign{ & = \left( {\frac{7}{8} \times 8t} \right) \cr & = 7t \cr} $$