Question

Rajdhani Train running at a speed of 54 km/hr crosses a platform of length same as that of the train in 36 sec. If a Duranto train, which is 230 meters long, crosses the same platform in 25 sec, then find speed of Duranto train (in km/hr)?

• A. 54 km/h
• B. 72 km/h
• C. 84 km/h
• D. 90 km/h

Hint:

To solve speed, time, and distance problems, use the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \) and convert units appropriately.

Answer 1

The Correct Option is B

Let the length of Rajdhani Train be \( L \) meters. It crosses a platform of length \( L \) meters in 36 seconds. The total distance covered by Rajdhani Train is \( 2L \) meters, and the speed of the train is 54 km/hr. Converting the speed into meters per second: \[ 54 \, \text{km/hr} = \frac{54 \times 1000}{3600} = 15 \, \text{m/s} \] Now, using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \): \[ 15 = \frac{2L}{36} \] \[ 2L = 540 \] \[ L = 270 \, \text{meters} \] Now, for the Duranto train, the total distance covered is the length of the Duranto train (230 meters) plus the length of the platform (270 meters), which is \( 230 + 270 = 500 \) meters. The time taken is 25 seconds. Using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \): \[ \text{Speed of Duranto} = \frac{500}{25} = 20 \, \text{m/s} \] Converting this back to km/hr: \[ 20 \, \text{m/s} = \frac{20 \times 3600}{1000} = 72 \, \text{km/hr} \] Thus, the speed of the Duranto train is \( \boxed{72} \) km/hr.