A car runs at 50 km/h when it has not been serviced and at 60 km/h after servicing. After servicing, it covers a certain distance in 6 hours. 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, before and after servicing a car. It is a direct application of the basic formula time = distance divided by speed, and it reinforces the idea that higher speed reduces travel time when distance remains constant.

Given Data / Assumptions:
Speed of the car after servicing = 60 km/h.
Speed of the car when not serviced = 50 km/h.
After servicing, the car covers a certain distance in 6 hours.
The distance is the same in both cases.
We must find the time taken by the car to cover the same distance when not serviced, at 50 km/h.

Concept / Approach:
First we calculate the distance covered after servicing using distance = speed * time. Then we use that distance with the lower speed (before servicing) to calculate the new time required. No complicated algebra is needed, only straightforward application of formulas with consistent units.

Step-by-Step Solution:
Step 1: Compute the distance travelled after servicing.Step 2: Distance D = speed * time = 60 km/h * 6 h.Step 3: D = 360 km.Step 4: For the unserviced car, speed = 50 km/h.Step 5: Time taken at 50 km/h to cover 360 km is time = distance / speed.Step 6: Time = 360 / 50 hours.Step 7: Simplify 360 / 50 = 36 / 5 = 7.2 hours.

Verification / Alternative check:
To check, multiply the unserviced speed by the computed time: 50 * 7.2 = 360 km, which matches the distance covered after servicing. This confirms that the distance is consistent in both situations and that the calculated time is correct. The small increase in time compared to 6 hours is logical because 50 km/h is slightly slower than 60 km/h.

Why Other Options Are Wrong:
8 hours and 8.2 hours represent more time than necessary. If the car took 8 hours at 50 km/h, it would travel 400 km, not 360 km.
6.5 hours is too small. At 50 km/h, 6.5 hours would give only 325 km, which is less than the required distance.
7 hours would still be short, giving 350 km, not the full 360 km.

Common Pitfalls:
Some learners incorrectly use proportions without first finding the exact distance, or they mix up which speed belongs to which time. Others may guess by rough reasoning rather than applying the formula precisely. Always compute the distance first using the known speed and time, then derive the second time from that distance and the second speed.

Final Answer:
The car will take 7.2 hours to cover the same distance when it has not been serviced.