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 3/4^{th} 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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Must Read Time, Speed and Distance Articles

- Time, Speed and Distance: Basic concepts
- Time, Speed and Distance- Basics
- Time, Speed and Distance: Problems on Trains

- Time, Speed, Distance: Circular Motion
- Time, Speed and Distance- Ratio Concept
- Relative Speed & Problems on Trains

**Example 3:** Amit & Bimal are at a distance of 800 m. They start towards each other @ 20 & 24 kmph. As they start, a bird sitting on the cap of Amit, starts flying towards Bimal, touches Bimal & then returns towards Amit & so on, till they meet. What is the distance traveled by the bird, if its speed is 176 kmph?

**Solution:** In this question, Amit and Bimal are moving towards each other. So their relative speed is 20 + 24 = 44 km/hr. The speed of the bird is 176 km/hr.

Now, the logic is simple. The bird flies for the same time as both Amit and Bimal take to meet.

Since the time taken by Amit and Bimal together and the bird is same, so the distance covered will be in the ratio of their speeds.

The ratio of the speeds is 44: 176 or 1: 4. Hence, if Amit and Bimal cover 800 m, the bird will cover 800*4 = 3200 m.

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**Key Learning:**

- 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 and time taken by the two objects to cover same distance will be in the ratio b:a.
- The ratio concept can be applied only when one of the given distance, time or speed is constant.

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