A bus can travel 20% faster than a scooter. Both start from point P at the same time, and reach point Q, 60 km away from point P, at the same time. On the way, however, the bus lost about 10 minutes while stopping at bus stations, while the scooter did not stop anywhere. What is the speed of the bus?

Let's assume the speed of a scooter is 'y' km/h.

A bus can travel 20% faster than a scooter.

speed of a bus = y of (100+20)%

= y of 120%

= $$y\times\frac{120}{100}$$

= 1.2y

When bus stopped for 10 minutes, then both of them will take the same time to cover 60 km distance.

So let's assume the original time (without stop) taken by bus to cover 60 km distance is 't' hours.

time taken by scooter to cover 60 km distance = $$\left(t+\frac{10}{60}\right)$$

speed of bus $$\times$$ time taken by bus to cover the distance = speed of scooter $$\times$$ time taken by scooter to cover the distance

$$1.2y \times t = y \times (t+\frac{10}{60})$$

$$1.2t=(t+\frac{1}{6})$$

$$1.2t-t=\frac{1}{6}$$

$$0.2t=\frac{1}{6}$$

Speed of the bus = $$\frac{distance}{time}$$

$$1.2y = \frac{60}{t}$$

Put Eq.(i) in the above equation.

$$1.2y = \frac{60}{\frac{1}{1.2}}$$

$$1.2y=60\times\ 1.2$$

y = 60

speed of the bus = 1.2y

= $$1.2\times60$$

= 72 km/h