Time, Speed and Distance- Ratio Concept

Learn the ratio concept to solve questions from time, speed and distance with the help of solved EXAMPLES

The concept of ratio is a very important tool while solving questions in any aptitude-based paper. A lot of calculations can be avoided by applying basic concepts of ratio. In this article we will learn to apply ratio to solve Time, Speed and Distance (TSD) questions.

Basic Concept

The basic formula says Speed= Distance/Time . From this formula, it is evident that speed is directly proportional to distance and inversely proportional to time.

Basically, it means if two objects have their speeds in the ratio a:b,

Distance covered by the two objects in same time will be in the ratio a:b;

Time taken by the two objects to cover same distance will be in the ratio b:a.

Let us apply this concept to some examples given below.

Solved Examples

Example 1: If I travelled at 3/4th of my average speed and reached 25 minutes late, what is the time that I usually take to reach my destination?

Solution: Although this question can be solved by making a simple EQUATION, still the use of ratio can eliminate the calculation-work.

Since, the current speed is 3/4th the average speed, we can take the current speed as 3km/hr and the average speed as 4km/hr so that the ratio of the speeds is 3:4.

As the distance covered is same in both the cases, so the time taken will be in the ratio 4:3 (in the reverse ratio of speeds).

It means that if today, I took 4 minutes then on an average I take 3 minutes i.e. I am one minute late.

Now apply simple chain RULE that, if I am late for 1 minute, the usual time taken is 3 minutes and if I am 25 minutes late, the normal time taken will be 25 x 3 = 75 minutes.

Example 2: A thief flees city A in a car towards city B on a stretch of straight road, 400 kilometers long, at a speed of 60 KM/hr. In 30 minutes a police party LEAVES city A to chase the thief at 80 km/hr. Find the distance travelled by the police when it catches thief.

Solution: In this question the thief travelled for the first 30 minutes. The speed of thief is 60 km/hr, so he has covered 30 km in 30 minutes.

The ratio of speeds of thief and police is 60: 80 or 3: 4.

Excluding the first 30 minutes, the thief and the police have run for the same time. So the distance covered is in the ratio of their speeds i.e. 3: 4.

Since, the initial distance between the thief and the police if 30 km, so in total, thief and police have covered 90 km and 120 km respectively (to make the ratio 3:4).

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