How to solve problems on rate change: CAT Quantitative Aptitude

On any rate problem involving — distance, rate, and time, you can always use the standard formula,  or some variation of the formula, thereof. Still, you must recognize the implicit information that helps you to solve the problem. But there may be a host of rate problems where the above formula does not fit. Let us go through some of such problems!

Example:
In a 1,000 metres race, Manish gives Ravi a start of 40 metres and beats him by 19 seconds. If Manish gives Ravi a start of 30 seconds then Ravi beats Manish by 40 metres. Find the ratio of speed of Manish to that of Ravi?

[1]  6/5
[2]  5/6
[3]  7/6
[4]  9/5

Solution:

  Hence, [3] is the correct option.

In another type of problem, the rate formula does not fit. An example is given below.

Example:

When a certain chemical reaction was allowed to run for t minutes, it produced a substance A(t) as shown in the following table.

Find the average rate of the production for the interval from t = 20 to t = 30.

[1] 1.61 moles/min
[2] 1.82 moles/min
[3] 1.94 moles/min
[4] 1.23 moles/min

Solution:
Average rate of reaction =   moles/min. Hence, [4] is the correct.

This topic also has some tricky ones like the following problem:

Example:

Radius of a spherical balloon, of radii 30 cm, increases at the rate of 2 cm per second. Then it’s curved surface increases by:

[1] 120
[2] 480
[3] 600
[4] None of these

Solution:
Curved surface are of sphere (balloon) and change in radius 

To get the rate of change we need to differentiate the value of curved surface are S.

Hence, choice [2] is correct.

After understanding the concept of Rate of change, aspirants need to practice a lot. They should include all kind of problems in their preparation. This will prepare them well for the different kind of questions which can be asked on the topic.