A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses

Step-by-step explanation:

Let the speed of cyclist be C and bus be B.

Using the concept of relative speed:-

For incoming bus, speed = B + C

For overtaking bus, speed = B - C

Now, distance travelled b/w 2 incoming bus = (B + C) * 4

Now, distance travelled b/w 2 overtaking bus = (B - C) * 12

so,

(B + C) * 4 = (B - C) * 12

or, B=2C

Hence, distance b/w two buses in same direction, d=4 * (3/2) B=6 B

Therefore, time gap=d/B=6 minutes