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## Percentage

Understand the concept of percentages with detailed explanations, examples, and real-life applications. Master percentage calculations for competitive exams and everyday use.

Percentages are an essential part of daily life, frequently encountered in shopping, finance, academics, and more. Understanding percentages not only helps you excel in competitive exams but also simplifies decision-making in real-life scenarios. In this blog, we’ll cover everything you need to know about percentages from the basic concept to advanced calculations and their application.

#### Percentage

### What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word “percent” comes from the Latin phrase *per centum*, meaning “by the hundred.” It’s used to compare values, show growth, or present proportions in a concise manner.

For example:

- 50% of a quantity means 50 out of 100.
- 75% means 75 out of 100.

**Formula for **Percentage = (Part / Whole) × 100

Section 2

## Types of Percentage Problems

In competitive exams and real life, percentage-related problems can be classified into a few major types:

**Finding the Percentage of a Number**

This type of problem asks you to find what percentage a given number represents of another number.

**Example 1:**

Find 25% of 200.

Solution: (25/100) × 200 = 50

**Example 2:**

Find 45% of 350.

Solution: (45/100) × 350 =157.5

**Finding What Percentage One Number is of Another**

This involves determining what percentage one number represents in comparison to another.

What percentage is 60 of 240?

Solution:(60/240) × 100 = 25%

**Increase or Decrease in Percentage**

This is one of the most common types of percentage problems. Here, you calculate by how much a quantity has increased or decreased in percentage.

**Example 1:**

A product’s price increases from $200 to $250. What is the percentage increase?

Solution: (250−200 / 200) × 100 = 25%

The price increased by 25%.

**Example 2:**

A company’s profits decreased from $5000 to $4500. What is the percentage decrease?

Solution: (5000−4500) / 5000 × 100 = 10%

So, the profits decreased by 10%.

Section 3

## Percentage Change in Real-Life Contexts

Understanding percentage change is crucial in various real-world situations, such as:

## Discounts and Sales

When shopping, discounts are usually presented as percentages. To calculate how much you save during a sale, you need to apply percentage calculations.

**Example:**

A store offers a 20% discount on a jacket priced at $100. What is the discounted price?

Solution: (20/100) × 100 = 20

The discount is $20, so the final price is $100 – $20 = $80.

## Interest Rates in Banking

In finance, percentages are used to represent interest rates. The interest you earn on your savings or the interest you pay on loans is calculated using percentage formulas.

**Example:**

You invest $1000 in a bank at an annual interest rate of 5%. How much interest will you earn in a year?

Solution: (5/100) × 1000 = 50

You will earn $50 in interest.

## Population Growth

Population changes are often expressed in percentage growth or decline.

**Example:**

If a city’s population grows from 1,000,000 to 1,050,000, what is the percentage increase?

Solution: (1,050,000−1,000,000 / 1,000,000) × 100 = 5%

## Exam Scores

Percentages are often used to express exam scores.

**Example:**

If a student scores 450 out of 600 in an exam, what percentage did they achieve?

Solution: (450/600) × 100 = 75%

The student scored 75%.

**Successive Percentage Change**

Sometimes, multiple percentage changes are applied one after another. In such cases, the successive percentage formula is used.

Net Percentage Change =

(1 + p1/100)(1 + p2/100)−1

Where:

- p1 and p2 are the successive percentage changes.

**Example:**

A product’s price is increased by 10% in the first month and then decreased by 5% in the second month. What is the net percentage change?

**Solution:**

Step 1:

Increase by 10%

Let the initial price be 100.

New price after 10% increase =

100 + 10/100 × 100 = 110

Step 2:

Decrease by 5%

New price after 5% decrease =

110 − 5/100 × 110 =104.5

Net percentage change =

(104.5−100) / 100 × 100 = 4.5%

Thus, the net effect is a 4.5% increase.

**Applications of Percentage in Competitive Exams**

Percentage problems are a major part of many competitive exams, including CAT, GMAT, SSC, and more. They often appear in the quantitative aptitude section. Understanding the key percentage concepts can help you solve more complex problems, like profit and loss, simple and compound interest, and data interpretation questions.

**Example:**

If the population of a town increases by 15% annually, and the current population is 40,000, what will be the population after 2 years?

**Solution:**

Use the successive percentage change formula:

**New population:**

=40000×(1+15/100)×(1+15/100)

= 40000 × 1.15 × 1.15 = 52900

Thus, the population after 2 years will be 52,900.

**Mistakes to Avoid in Percentage Calculations**

**Not understanding the base value**: When calculating percentages, always clarify what your base value is. For example, when talking about salary increases, is the percentage based on the initial salary or the new salary?

**Confusing percentage increase with simple addition**: If something increases by 20% twice, it doesn’t mean it increased by 40%. Use the successive percentage change formula instead.

**Forgetting to divide by 100**: When converting from percentages to numbers, always divide the percentage value by 100.

MCQ Test

### Number Systems Quiz

Here are 30 basic-level General Aptitude questions, each with multiple-choice options and detailed answers

Section 4

## Conclusion

Mastering percentages is not only crucial for cracking exams but also for day-to-day problem-solving. From calculating discounts while shopping to understanding financial growth, percentages help us make informed decisions. By practicing percentage-related problems and remembering the basic formulas, you can easily become proficient in this topic.

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