A car travelling at an average speed of 72 km/h takes 9 minutes to cover a certain distance on a straight road. If the car wants to cover the same distance in only 8 minutes, by how many km/h must it increase its average speed?

Introduction / Context:
This question examines the relationship between speed and time when the distance is fixed. It is a very common type in aptitude tests where the candidate must determine the new speed required to cover the same distance in a shorter time. It requires careful unit conversion from minutes to hours and accurate use of the formula distance = speed * time.

Given Data / Assumptions:

Initial average speed of the car = 72 km/h.
Time taken at this speed = 9 minutes.
The distance remains the same for the second case.
Desired time for the second case = 8 minutes.
Speeds are assumed to be constant in each case.
We need the increase in speed in km/h, that is new speed minus old speed.

Concept / Approach:
For a fixed distance, speed and time are inversely proportional. First, we compute the actual distance using the initial speed and time. Next, we divide this same distance by the new, shorter time to get the required new speed. The difference between this new speed and the original speed is the increase in speed. Time values must be converted from minutes to hours to maintain consistency with km/h units.

Step-by-Step Solution:
Step 1: Convert 9 minutes into hours: 9 minutes = 9 / 60 hours = 0.15 hours. Step 2: Compute the distance covered at 72 km/h in 0.15 hours: distance = 72 * 0.15. Step 3: Calculate 72 * 0.15 = 10.8 kilometres. Step 4: Convert the desired time of 8 minutes to hours: 8 minutes = 8 / 60 hours = 2 / 15 hours. Step 5: Required new speed = same distance / new time = 10.8 / (2 / 15) km/h. Step 6: Simplify 10.8 / (2 / 15) = 10.8 * (15 / 2) = 10.8 * 7.5 = 81 km/h. Step 7: Increase in speed = 81 − 72 = 9 km/h.

Verification / Alternative check:
Check that at 81 km/h for 8 minutes the car travels the same distance. Time in hours = 8 / 60 = 2 / 15 hours. Distance = 81 * (2 / 15) = 162 / 15 = 10.8 kilometres, which matches the original distance. This confirms that 81 km/h is the correct new speed and that the required increase is indeed 9 km/h.

Why Other Options Are Wrong:
An increase of 8 km/h would give a new speed of 80 km/h and a distance of 80 * (2 / 15) = 160 / 15 = 10.67 km, which is too small. Similarly, increases of 6 or 7 km/h produce distances smaller than 10.8 km in 8 minutes. An increase of 10 km/h results in a speed of 82 km/h, giving 82 * (2 / 15) ≠ 10.8. Only an increase of 9 km/h yields the exact required distance in the shorter time.

Common Pitfalls:
A common mistake is to directly scale the speeds by the ratio of times without computing the distance properly, which can lead to rounding or conceptual errors. Another frequent error is forgetting to convert minutes to hours or miscalculating 9 / 60 and 8 / 60. Careful attention to units and consistent use of the distance formula avoids such problems.

Final Answer:
The car must increase its speed by 9 km/h to cover the distance in 8 minutes instead of 9 minutes.