To cover a distance of 416 km, a train A takes $$2\frac{2}{3}$$ hours more than train B. If the speed of A is doubled, it would take $$1\frac{1}{3}$$ hours less than B. What is the speed (in km/h) of train A?

Let the speed of the train A be x km/hr
Ratio of speed of the A before to after = x : 2x
As we know,
Time is inversely proportional to speed.
Ratio of time of A before to after to cover distance = 2x : x
Time difference = 2x - x = $$2\frac{2}{3} + 1\frac{1}{3}$$
⇒ x = $$\frac{8}{3} + \frac{4}{3}$$
⇒ x = $$\frac{{12}}{3}$$
⇒ x = 4 hr
Time taken by A to cover distance = 2x = 2 × 4 = 8 hr
∴ Speed of train A = $$\frac{{416}}{8}$$ = 52 km/hr