Question

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kilometres 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 kmph
• B. 110 kmph
• C. 120 kmph
• D. 130 kmph

Answer 1

Answer: (C)

120 km/h

Step 1, Given data

Speed of the train is 50% more than the speed of the car

Distance = 75 km

Time lost by the train = 12.5 min = $\frac{12.5}{60}h$

Step 2, Finding the speed

Let the speed of the car be x kmph.

Then, speed of the train $=\frac{150x}{100}=\frac{3x}{2}$ km/h

According to the question

$\therefore \frac{75}{2}-\frac{75}{\left(\frac{3}{2}\right)x}=\frac{125}{10\times 60}$

$\Rightarrow \frac{75}{x}-\frac{50}{x}=\frac{5}{24}$

After solving

$\Rightarrow x=\left[\frac{25\times 24}{50}\right]$ = 120 km/h

Hence the speed of the car is 120 km/h