Learn and understand problems on Relative Motion: CAT Quantitative Aptitude

This article focuses on the concept of ‘Relative Motion Between Two Bodies’. Such questions have been part of the CAT paper and should not be neglected as they are really easy to score on.

Basic Concepts (Time, Speed and Distance)

• If the speed of a body is changed in the ratio x:y, then the time taken by the body is changed in the ratio y:x, assuming the distance is constant
• If the speed remains constant and the time for which a body is in motion is changed in a certain ratio x:y then the distance is changed in the same ratio x:y
• In a fixed time and given a change in distance in the ratio x:y, the speed is also changed in the ratio x:y
• Change in Speed:At times during a journey, the speed of a body will vary (increase or decrease). In this case, the journey should be broken down into sections. Each section of the journey should be such that the speed of the body in that section is a constant
• Average Speed:If the speed changes several times during a journey, then we introduce the idea of average speed. The formula for average speed, which we will

             denote by Speed_avg or S_avg is, 

Relative Speed

The idea of relative speed arises when two bodies are in motion. The relative speed, which is denoted by S_r, is defined as follows:

Let A and B be the two bodies. Let their speeds be SA and SB respectively. Then,

(i)    S_r = S_A + S_B, if they are travelling in opposite directions
       (in the opposite direction the relative speed or effective speed between two bodies is the sum of their speeds)

(ii)    S_r = S_A - S_B, if they are travelling in the same direction
       (in the same direction the relative speed or effective speed between two bodies is the difference of their speeds)

Note:

The concept of ‘to and fro’ motion in a straight line, is also an extension of the concept of relative motion between two bodies

Example:

Two racing cars have a relative speed of 12 km per hour. If the faster car travels at a speed of 164 km per hour, what is the speed of the slower car?

Solution:

The cars travel in the same direction.The relative speed is 12km per hour.
Thus, the speed of the slower car is 164 - 12 = 152 km per hour