A train travels 20% faster than a car. Both start from point A at the same time and reach point B, 180 km away at the same time. On the way the train takes 30 minutes for stopping at the stations. What is the speed (in km/hr) of the train?

Let speed of car = $$100x$$ km/hr

=> Speed of train = $$100x\times\frac{120}{100}=120x$$ km/hr

Total time taken by train to reach point B = $$(\frac{180}{120x}+\frac{30}{60})$$ hours

and time taken by car = $$\frac{180}{100x}$$ hours

According to ques,

=> $$\frac{180}{120x}+\frac{1}{2}=\frac{180}{100x}$$

=> $$\frac{180}{100x}-\frac{180}{120x}=\frac{1}{2}$$

=> $$\frac{180}{20x}(\frac{1}{5}-\frac{1}{6})=\frac{1}{2}$$

=> $$\frac{9}{x}(\frac{1}{30})=\frac{1}{2}$$

=> $$x=\frac{18}{30}=\frac{3}{5}$$

$$\therefore$$ Speed of train = $$120\times\frac{3}{5}=72$$ km/hr

=> Ans - (C)