A person takes 20 minutes more to cover a certain fixed distance when he decreases his speed by 20 percent. What is the time taken to cover the distance at his original speed?

Introduction / Context:
This is a time, speed and distance problem involving a percentage change in speed. We know how much extra time is taken when the person reduces speed by 20 percent. Using this information, we must find the original time taken to cover the same fixed distance at the original speed.

Given Data / Assumptions:

• The distance is fixed and does not change between scenarios.
• Original speed is v km/h and original time is t hours.
• New speed after reduction is 20 percent less than v, that is 0.8v.
• New time is 20 minutes more than the original time.
• 20 minutes is 20 / 60 = 1/3 hour.

Concept / Approach:
For the same distance, speed and time are inversely proportional: distance = speed * time. When speed is multiplied by a factor, time is divided by the same factor. Reducing speed by 20 percent to 0.8v increases time by a factor of 1 / 0.8 = 1.25. We translate the given 20 minute increase into an equation involving t and solve for t.

Step-by-Step Solution:
Let original time be t hours at speed v. Original distance D = v * t. New speed after reduction = 0.8v. Since D is unchanged, new time t_new satisfies v * t = 0.8v * t_new, so t_new = t / 0.8 = 1.25t. Given that the new time is 20 minutes more than the original, t_new = t + 1/3 hours. So 1.25t = t + 1/3. Subtract t from both sides: 1.25t - t = 1/3 gives 0.25t = 1/3. Solve for t: t = (1/3) / 0.25 = (1/3) * 4 = 4/3 hours. Convert 4/3 hours to minutes: 4/3 * 60 = 80 minutes = 1 hour 20 minutes.

Verification / Alternative check:
Original time t = 1 hour 20 minutes. New time t_new = 1.25t = 1.25 * (4/3) hours = 5/3 hours = 100 minutes. The difference between 100 minutes and 80 minutes is 20 minutes, matching the question statement.

Why Other Options Are Wrong:
If the original time were 1 hour, then a 25 percent increase would give 1 hour 15 minutes, not 20 minutes extra. Options 1 hour 10 minutes, 50 minutes and 40 minutes similarly do not give an increase of exactly 20 minutes when multiplied by 1.25. Only 1 hour 20 minutes satisfies the proportional change implied by the speed reduction.

Common Pitfalls:
Learners may mistakenly treat the 20 percent change as a direct difference in time rather than applying it to speed and using inverse proportionality. Forgetting to convert 20 minutes into hours before forming equations can also lead to errors. Always express times in a single unit when working with such relationships.

Final Answer:
The time taken at the original speed is 1 hour 20 minutes.