A taxi travels at 90 km/h and takes 35 minutes to cover a certain distance. By how many kilometres per hour should it increase its speed to cover the same distance in only 21 minutes?

Introduction / Context:

This question tests the core time, speed and distance relationship that is heavily used in quantitative aptitude and competitive exams. The situation describes a taxi that initially travels at a given constant speed and takes a known time to cover an unknown distance. Then we are asked how much the speed must be increased so that the same distance is covered in a shorter time. Understanding how speed changes when time changes for a fixed distance is a very important concept for solving many real life travel and motion problems in exams.

Given Data / Assumptions:

• Initial speed of the taxi = 90 km/h.
• Time taken at this speed = 35 minutes.
• The distance remains the same in both journeys.
• Required time for the same distance = 21 minutes.
• We need the increase in speed in km/h, not just the new speed.

Concept / Approach:

For any uniform motion, the basic relation is distance = speed * time. When the distance is fixed, speed is inversely proportional to time. That means if time decreases, speed must increase in a specific ratio so that distance remains unchanged. We first compute the original distance using the initial speed and time. Then we compute the new speed required to cover that same distance in the shorter time. Finally, we subtract the old speed from the new speed to find the increase in speed in km/h.

Step-by-Step Solution:

Verification / Alternative check:

We can verify by checking that at 150 km/h the taxi really needs only 21 minutes. Time = distance / speed = 52.5 / 150 hours. This is equal to 0.35 hours. Converting 0.35 hours into minutes gives 0.35 * 60 = 21 minutes, which matches the required time. The calculations are therefore consistent and confirm that the increase in speed must be 60 km/h.

Why Other Options Are Wrong:

Option 150 represents the new speed, not the increase in speed, so it does not answer the exact question. Option 120 km/h would still not reduce the time enough, because 52.5 / 120 hours is more than 21 minutes. Option 90 km/h is simply the original speed and would not reduce the travel time at all. Therefore all other options fail to satisfy the condition of covering the same distance in only 21 minutes.

Common Pitfalls:

Many learners forget to convert minutes into hours before applying the speed formula, which leads to wrong numerical values. Another common mistake is to compute only the new speed and select that as the answer, even though the question specifically asks for the increase in speed. It is also easy to mix up the proportional reasoning and think that the speed increases by the same number of minutes reduced, which is not correct. Always compute the distance first or use ratios carefully.

Final Answer:

The taxi must increase its speed by 60 km/h to cover the same distance in 21 minutes.