Q 2 towns A & B are connected by regular bus service with a bus leaving in either direction in every T minute. A man cycling with a speed of 20 km/h in a direction A to B, notice that a bus goes passed him every 18 min in the direction of his motion & every 6 min in opposite direction. What is period T of the bus service and with what speed do the buses ply on the road?

Let V be the speed of the bus running between towns A and B.

Speed of the cyclist, v = 20 km/h

Relative speed of the bus moving in the direction of the cyclist

= V – v = (V – 20) km/h

The bus went past the cyclist every 18 min i.e., (when he moves in the direction of the bus).

Distance covered by the bus =  … (i)

Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to 

Both equations (i) and (ii) are equal.

Relative speed of the bus moving in the opposite direction of the cyclist

= (V + 20) km/h

Time taken by the bus to go past the cyclist 

From equations (iii) and (iv), we get

Substituting the value of V in equation (iv), we get