Percentage Concepts

Understanding the Concepts of Percentage

Percentage are an essential and high-weightage concept in aptitude-based assessments. Many problems in other aptitude topics, like Profit and Loss, Simple Interest, Compound Interest, and Data Interpretation can be addressed with a good understanding of percentage.

There are three main types of problems or concepts in percentage; they are

1. Calculation Based
2. % Increase Decrease
3. % Successive Increase Decrease

We will understand each of these with an example

1. Calculation Based

These are problems that need direct calculations. It will be found commonly in simplification problems. Understanding these concepts will help us address data interpretation challenges and perform real-world calculations.

Sample questions will look like these - Find 33.33% of 24 + 25% of 32.

These difficulties are readily handled by understanding percentage to a fractional value, approximation, and elimination approaches utilising digital sum. (These approaches will not work for all problems.)

Fractional Value Techniques

Certain percentage values can be replaced with fractions, and that will enable us to solve the problems faster.

In the above example,

• 33.33% can be written as ⅓ rd of a number,
• 25% can be written as ¼ that of a number

So applying these, we will be able to rewrite the problem as

(⅓ * 24) + ( ¼ * 32),

which can be easily simplified as 8 + 8, and the answer is 16.

So it's advisable to remember standard fractional values of percentages to solve some problems faster.

Given below is a standard percentage to fractions table to remember.

Approximation and elimination procedures are rational thinking techniques for guessing answer choices when they are distant from one other.

In the above example, for 33.33% of 24, we can roughly guess

• 10% of 24 as 2.4,
• And 30% will be 7.2,
• And 33.33% of 24 will be slightly more than 7.2, so we can take 8 for ease of calculation.

2. % Increase Decrease

In these types of concepts, one percentage increase will be given, and a corresponding percentage decrease will be asked or vice-versa. Both the parameters will be inversely proportional to each other.

Example Problem

Arvind has 25 % more rupees than Pinku. How much percent less rupees does Pinku have as compared to Arvind?

These types of problems can be solved by learning percentage change concepts.

General percentage change formula,

*Percentage change = [(change in value)/(base value)]100

In the above example, let's assume that Pinku has Rs. 100, so we know Arvind will have Rs. 125 from the given data.

% change = [[125-100(this is the change in value)]/[125(here we are comparing with Arvind, so the base value is 125]] * 100

We get = [25/125]*100 ⇒ 20% is the answer.

3. % Successive Increase Decrease

In these types of multiple percentage increases/decreases, values will be given, and questions will be asked based on the percentage change.

Example Problem

In an election between two candidates, 20% of the votes were invalid, one got 55% of the total valid votes. If the total number of votes was 7500, the number of valid votes that the other candidate got, was?

These types of problems can be solved using many approaches, but a simple formula that will help us to solve these problems is given below,

If the value of an object x is successively changed by a%, b%, and then by c%, the final value is x (1 ± a/100) (1 ± b/100) (1 ± c/100),

where

positive sign (+) indicates an increment

negative sign (-) indicates a decrement.

Applying the above in the example, we get

= 7500 ( (1 - (20/100)) (1 -(55/100)) or

Simply we can write this as,

= 7500 (80/100) (45/100)

= 2700 is the answer