A bike runs at a speed of 35 km/h when it has not been serviced and at 55 km/h after servicing. After servicing, the bike covers a certain distance in 5 hours. Approximately how much time will it take to cover the same distance when it has not been serviced?

Introduction / Context:
This question compares the time taken to cover the same distance at two different speeds. It tests the basic relationship between speed, distance, and time and also asks for an approximate value. Such problems are common in speed and distance sections and help you build intuition about how travel time changes with speed.

Given Data / Assumptions:
- Speed of the bike after servicing = 55 km/h.
- Time taken after servicing to cover the distance = 5 hours.
- Speed of the bike before servicing = 35 km/h.
- The distance covered in both cases is the same.
- We are asked for the approximate time taken at 35 km/h to cover that distance.

Concept / Approach:
First, we use the post-service speed and time to find the actual distance. Then, we use the pre-service speed and the same distance to find the required time. The core formula is distance = speed * time. The final answer is expressed as an approximate time, so a small rounding is acceptable if needed.

Step-by-Step Solution:
Step 1: Compute the distance using the post-service data.Distance = speed * time = 55 km/h * 5 h = 275 km.Step 2: Use the pre-service speed to find the time for the same distance.Pre-service speed = 35 km/h.Time at 35 km/h = distance / speed = 275 km / 35 km/h.Step 3: Simplify 275 / 35.275 / 35 = 55 / 7 ≈ 7.857 hours.Step 4: Round off 7.857 hours to the nearest option. The closest given option is 8 hours.

Verification / Alternative check:
We can roughly estimate: at 35 km/h, in 8 hours the bike would cover 35 * 8 = 280 km, which is very close to 275 km. At 7.5 hours, the distance would be 35 * 7.5 = 262.5 km, which is farther from 275 km. This comparison confirms that 8 hours is the best approximate choice among the options.

Why Other Options Are Wrong:
- 7.5 hours corresponds to about 262.5 km, which is too short compared to 275 km.
- 7 hours gives 245 km, and 6.5 hours gives 227.5 km, both significantly smaller than 275 km.
- Therefore, these options do not represent the correct time for covering the same distance at 35 km/h.

Common Pitfalls:
Some candidates forget that the distance remains constant and mistakenly try to average speeds instead of using distance and time properly. Others miscalculate 275 / 35 due to fraction handling errors. A good habit is to first find the distance using one scenario and then reuse that distance in the second scenario, rather than trying to jump directly to a ratio without clear steps.

Final Answer:
The bike will take approximately 8 hours to cover the same distance when not serviced.