Question

A train can travel 50% faster than a car Both start from point A at the same time and reach point B 75 km 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

• A. 100 km/hr
• B. 110 km/hr
• C. 120 km/hr
• D. 130 km/hr

Answer 1

The correct option is C 120 km/hr

Let the speed of the car be x km/hr Then speed of the train $=x+\frac{50}{100}x=\frac{150x}{100}km/hr=\frac{3x}{2}km/hr$

Time taken by car to reach point B = $\frac{75}{x}hrs$

Time taken by train to reach point B = $\frac{75}{\frac{3}{2}x}hrs$

Given $\frac{75}{x}-\frac{75}{\frac{3}{2}x}=\frac{12.5}{60}$

$\Rightarrow \frac{75}{x}-\frac{50}{x}=\frac{125}{10\times 60}=\frac{5}{24}$

$\Rightarrow \frac{25}{x}=\frac{5}{24}$

$\Rightarrow \Rightarrow x=\frac{25\times 24}{5}=120km/hr$