A bus covers a certain journey in 10 hours at a constant speed of 80 km/h. If the same distance has to be covered in only 4 hours, what should be the new speed of the bus (in km/h)?

Introduction / Context:
This time and distance aptitude question tests the fundamental relationship between speed, time, and distance when the distance is fixed. You are given the original speed and time taken by a bus to complete a journey and then asked to find the new speed required to cover the same distance in a shorter time. Understanding this relationship is very important for competitive exams and everyday reasoning about travel planning.

Given Data / Assumptions:
- The bus travels at a constant speed of 80 km/h in the first situation.
- Time taken in the first situation is 10 hours.
- The distance of the journey remains the same in both situations.
- In the second situation, the time allowed is only 4 hours.
- We assume no delays, no breaks, and a straight journey at uniform speed in both cases.

Concept / Approach:
The key concept used here is the standard formula for motion in one dimension:
distance = speed * time.
When the distance is the same in two different scenarios, the product of speed and time must also be the same. Therefore, if the time decreases, the speed must increase proportionally to keep the distance constant. This inverse relationship between speed and time for a fixed distance is at the heart of this question.

Step-by-Step Solution:
Step 1: Compute the distance of the journey in the first case.Distance = speed * time = 80 km/h * 10 h = 800 km.Step 2: Let the required new speed be v km/h in the second case.The distance is the same, so: v * 4 h = 800 km.Step 3: Solve for v: v = 800 / 4 = 200 km/h.Therefore, to cover the same 800 km in 4 hours, the bus must travel at 200 km/h.

Verification / Alternative check:
If the bus actually moves at 200 km/h for 4 hours, the distance covered = 200 * 4 = 800 km, which matches the original distance. This confirms the correctness of the calculation. Also, the time has become less than half (from 10 hours to 4 hours), and the speed has become more than double (from 80 km/h to 200 km/h), which is consistent with the inverse relationship between speed and time for fixed distance.

Why Other Options Are Wrong:
- 120 km/h would cover only 120 * 4 = 480 km, which is less than the required distance of 800 km.
- 160 km/h would cover 160 * 4 = 640 km, still short of 800 km.
- 180 km/h would cover 180 * 4 = 720 km, which again does not reach 800 km.
Only 200 km/h gives exactly 800 km in 4 hours.

Common Pitfalls:
Candidates often confuse “increase in speed” with “new speed” and may try to directly work on the difference without first computing the distance. Another common mistake is to think that if the time becomes 4/10 of the original, the speed should just be multiplied by 10/4 without verifying with the distance. The safest method is always to compute the distance first and then apply distance = speed * time in the new situation.

Final Answer:
The new speed required is 200 km/h.