A man reduces his travelling time by a fraction of 2/5, and as a result the distance covered by him increases by 20%. By what percentage does the speed of the man increase?

Introduction / Context:
This problem combines the core concepts of speed, distance and time with percentage changes. The question states that a man reduces his travel time and simultaneously increases the distance he covers. The task is to determine the resulting percentage increase in speed. Such questions are common in aptitude tests because they check understanding of the proportional relationship between speed, distance and time, as well as the correct handling of successive percentage changes.

Given Data / Assumptions:

Let the initial time taken be T hours.
Let the initial distance travelled be D kilometres (or any unit).
Initial speed v = D / T.
Travelling time is reduced by a fraction of 2 / 5, so new time = (1 - 2 / 5) * T = 3T / 5.
Distance travelled increases by 20%, so new distance = 1.2D.
New speed v new = new distance / new time.

Concept / Approach:
The key relationship is speed = distance / time. When time and distance change together, speed changes according to their combined effect. We express the new time and new distance as multiples of the original values, then form the ratio new speed divided by old speed. Finally we convert this ratio into a percentage increase. Handling the fraction 2 / 5 and 20% carefully is crucial for arriving at the correct result.

Step-by-Step Solution:
Initial speed v = D / T.New time = 3T / 5 (because time is reduced by 2 / 5 of T).New distance = 1.2D (a 20% increase over D).New speed v new = (1.2D) / (3T / 5).Simplify: v new = 1.2D * (5 / 3T) = (1.2 * 5 / 3) * (D / T).Compute the numeric factor: 1.2 * 5 = 6, and 6 / 3 = 2.Therefore v new = 2 * (D / T) = 2v.So the new speed is twice the old speed, which is a 100% increase.

Verification / Alternative check:
We can test with simple numbers. Suppose initially D = 100 km and T = 5 hours, so v = 20 km per hour. New time = 3 / 5 of 5 = 3 hours. New distance = 1.2 * 100 = 120 km. New speed = 120 / 3 = 40 km per hour. Since 40 is exactly double 20, the speed has increased by 20 km per hour, that is 100%. This numerical example confirms our algebraic result.

Why Other Options Are Wrong:

77% and 88% correspond to incorrect combinations of the percentage changes and usually come from partial or incorrect multiplication of factors.
99% is a near miss and often appears when rounding mistakes are made, but the exact calculation shows a clean doubling of speed, not a 99% increase.
60% does not match any logical calculation from the given data and reflects a misunderstanding of how speed depends on both distance and time.

Common Pitfalls:
Many learners subtract or add percentages directly, or they treat time and distance changes as if they affect speed independently. Another mistake is to apply the 2 / 5 reduction as 2 / 5 of the new time instead of the original time. Forgetting that a reduction in time increases speed and an increase in distance also increases speed can lead to sign errors. Always express new quantities as clear multiples of the old values before forming the speed ratio.

Final Answer:
The new speed is twice the original speed, so the percentage increase in the speed of the man is 100%.