Question

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

• A. 100 kmph
• B. 110 kmph
• C. 120 kmph
• D. 130 kmph

Hint:

When speeds differ and arrival time is same, adjust time using delays carefully.

Answer 1

The Correct Option is C

Concept: Use relation between speeds and time, considering delay.
Step 1: Assume car speed = $x$ kmph.
\[ {Train speed} = 1.5x \]
Step 2: Time taken without delay.
\[ {Car time} = \frac{75}{x}, \quad {Train time} = \frac{75}{1.5x} = \frac{50}{x} \]
Step 3: Include delay of train.
\[ {Delay} = 12.5 { min} = \frac{12.5}{60} = \frac{1}{4.8} \approx 0.2083 { hr} \] Since both arrive at same time: \[ \frac{75}{x} = \frac{50}{x} + 0.2083 \]
Step 4: Solve equation.
\[ \frac{75 - 50}{x} = 0.2083 \Rightarrow \frac{25}{x} = 0.2083 \Rightarrow x \approx 120 \]
Hence, the speed of the car is 120 kmph.