A train started from A to B with a speed of 20 km/h , then from B to C (where BC = 2AB) with a speed of 60 km/h , and returns from C to A with a speed of 10 km/h. What is the average speed (in km/h) of the train during the entire journey ?

\(\frac{360}{23}\)

Total distance = x + 2x + 3x

Distance = Speed × Time 

Total time = \(\frac{x}{20}\) + \(\frac{2x}{60}\) + \(\frac{3x}{10}\)

                = \(\frac{23x}{60}\)

Avg. speed = \(\frac{Total\;Distance}{Total\;Time\;Taken}\)

                 = \(\frac{x \;+\; 2x\; +\; 3x}{\frac{23}{60}}\)

                 = \(\frac{360}{23}\)