The Shatabdi Express runs from Kolkata to Ranchi at an average speed of 80 km/h and takes 7 hours for the journey. What is the distance between Kolkata and Ranchi in kilometres?

Introduction / Context:

This question is a direct application of the basic time and distance formula. It provides the average speed of a train and the time taken for a journey between two cities and asks for the distance. Such problems are standard in aptitude tests and help in building confidence with straight forward calculations involving speed, time and distance.

Given Data / Assumptions:

• Average speed of the Shatabdi Express = 80 km/h.
• Time taken for the journey = 7 hours.
• Motion is assumed to be uniform at the given average speed.
• We need the distance in kilometres between Kolkata and Ranchi.

Concept / Approach:

The foundational formula is distance = speed * time. When both speed and time are known and expressed in compatible units, distance can be found simply by multiplying. Here speed is in kilometres per hour and time is in hours, so the resulting distance will naturally be in kilometres. There is no need for unit conversions because the units already match.

Step-by-Step Solution:

Verification / Alternative check:

As a quick check, if the train travels at 80 km in each hour, in 5 hours it would cover 400 km and in 2 more hours it would cover 160 km more. Together this becomes 400 + 160 = 560 km. This mental verification confirms that the multiplication 80 * 7 has been done correctly and the obtained distance is logical for such a journey.

Why Other Options Are Wrong:

Option 506 km does not come from any simple product involving 80 and an integer number of hours, so it is not correct. Options 560 m and 650 m are in metres, which are far too small for a long distance train journey between cities like Kolkata and Ranchi. The units in those options do not match the realistic scale of the trip. Therefore only 560 km is consistent with the given speed and time.

Common Pitfalls:

Students sometimes confuse hours and minutes or think they need to convert units when it is not necessary. Here both speed and time are already in compatible units. Another mistake is to miscalculate 80 * 7 as 5600 or 480 by misplacing a zero or adding incorrectly. It is always a good idea to quickly break the multiplication into 8 * 7 = 56 and then append the zero.

Final Answer:

The distance between Kolkata and Ranchi is 560 kilometres.