Speed, distance and Time concepts and tricks| Math shortcuts for competitive exams

Speed Distance and Time
Quantitative aptitude questions related to speed, distance, and time are frequently asked in various competitive exams and job interviews. To solve these problems, it is important to understand the basic formulae and concepts related to speed, distance, and time.

One must also be able to convert between different units of measurement, such as kilometers per hour (km/hr) and meters per second (m/s). Practice and familiarity with common types of problems, such as those involving relative speed, average speed, and round-trip journeys, can also help improve one's ability to solve speed, distance, and time problems quickly and accurately.

Basic Formula
Let a person running with a speed of 's' cover a distance from A to B in time 't'. Here AB = d.

Then, Distance= Speed×Time
d=s×t

Proportionality between speed, distance, and time
Here we will explore the relationship between speed, distance, and time in three different scenarios.

Case 1: Distance is constant
If the distance is fixed then speed is inversely proportional to time.

Case 2: Speed is constant
Distance ∝ Time
If the speed is constant, then the distance is proportional to the time.

Case 3: Time is constant
Distance ∝ Speed
It means that if the time is constant, then the distance is proportional to the speed.
Que 1: Ramesh reaches his office 16 minutes late at three fourth of his normal speed. Find the normal time taken by him to cover the distance between his home and his office.
Answer: 48 min

Que 2: Ram and Shyam cover the same distance at the speed of 6 km/hr and 10 km/hr respectively. If Ram takes 30 minutes more than Shyam, find the distance covered by each.
Distance= 7.5 km

Que 3: If Rohan reduces his speed by 5 km/h, he will take four hours more to reach the destination. If he increases his speed by 5 km/h, he will take 2 hours less to reach the destination. Find the normal time taken by him.
The normal time taken to complete the journey= 8 hr

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