A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{car}}\,{\text{be}}\,x\,kmph \cr & {\text{Then,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}} \cr & = \frac{{150}}{{100}}x = {\frac{3}{2}x} \,kmph \cr & \therefore \frac{{75}}{x} - \frac{{75}}{{\left( {3/2} \right)x}} = \frac{{125}}{{10 \times 60}} \cr & \Rightarrow \frac{{75}}{x} - \frac{{50}}{x} = \frac{5}{{24}} \cr & \Rightarrow x = {\frac{{25 \times 24}}{5}} \cr & \Rightarrow x = 120\,kmph \cr} $$