Percentage is one of the topics in Quants section of CAT and other entrance examinations. The best part about this topic is that all you need to know are the basics and what is even better is that you have already learnt them in school. Also a lot of other topics like Simple Interest/Compound Interest, Geometry etc have questions coming from this topic. So it not wise or advisable to leave this topic.
One of the challenges with percentage questions on the CAT is often the wording of the question itself. The mathematical calculations required to solve the questions are often not that hard.
Consider the following question:
Last year a company made a 20% profit on sales. This year’s sales are 30% higher than those of last year, but profits are only 15% of sales. This year’s profits are what percentage of last year’s?
How to solve percentage questions like these on the CAT
A quick way to solve percentage questions is by picking numbers. In percentage questions the best number to pick is usually 100. Start with last year’s sales at 100. Then your calculations of profits and sales increases become so simple they should be able to be done in your head.
Set up a simple table:
|
Sales |
Profit |
| Last Year |
100 |
20 |
| This Year |
130 |
19.5 (15% of 130 is 19.5) |
Express 19.5 / 20 as a percentage.
19.5 / 20 = x / 100
Multiply 19.5 / 20 by 5 / 5
The result is 97.5 / 100
Thus, the answer to the question is 97.5%.
How to solve geometry questions involving percentages
A variation on the above question is to ask about percentages and geometric figures. For example:
If the length of a rectangle is increased by 40% and the width is decreased by 40%, by what percentage does the area increase or decrease?
Start with a simple example of a rectangle with an area of 100.
Use simple values for the length and width. Let’s say 20 and 5.
Calculate the percentage changes: 40% of 20 is 8, and 40% of 5 is 2. As such, the length and width of the new rectangle will therefore be 28 and 3.
Calculate the area: 28 x 3 = 84.
From the original area of 100 to the new area of 84, the area thus decreases by 16%.
You can pick any number you like to start with when doing percentages questions. However, if you start with 100, life will become easier!
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