Introduction
This chapter delves into one of the fundamental aspects of quantitative reasoning: Percentage. This concept refers to a mathematical notation used to express a number as a fraction of 100. It is a widely used mathematical tool that aids comparison and helps in understanding numerous everyday situations such as discount calculation, tax computation, and data interpretation.
Importance in SSC, RRB, and Banking Exams
Percentage is a key topic in competitive examinations such as SSC, RRB, and Banking Exams. It forms the basis for various other topics like Profit & Loss, Simple & Compound Interest, and Data Interpretation. Thus, a sound understanding of percentage is essential for aspirants aiming for a high score in the Quantitative Aptitude section of these exams.
Basic Formulas and Concepts
The basic formula to calculate the percentage is as follows:
Percentage (P%) = (Value/Total value) x 100
Here are some other important concepts related to percentages:
- Increase Percentage: (Increase in value / Original value) x 100
- Decrease Percentage: (Decrease in value / Original value) x 100
- Percentage Change: [(New Value – Original Value) / Original Value] x 100
Advanced Concepts and Problem Types
Some of the advanced concepts and types of problems you will encounter related to percentages are:
- Profit and Loss: These problems involve the calculation of the percentage profit or loss made on a transaction.
- Simple and Compound Interest: Here, the percentage is used to calculate the interest accrued on a certain amount of money over a specific period.
- Data Interpretation: These problems involve the interpretation of graphical or tabular data, where percentage is often used to compare different data points.
- Mixture and Alligation: These problems involve the use of percentage to calculate the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price.
10.5 Problem-Solving Techniques and Examples
Let’s discuss a few types of problems and how to solve them:
Calculation of Percentage
Example: If a student scores 250 marks out of 300, what percentage does she score?
Here, we use the basic percentage formula. The value is 250, and the total value is 300. So, the percentage is (250/300) x 100 = 83.33%.
Profit and Loss
Example: A shopkeeper sells a shirt for Rs.200, making a profit of 25%. Find the cost price of the shirt.
In this problem, we know the selling price (Rs.200) and the profit percentage (25%). The cost price can be calculated using the formula:
Cost price = Selling price / (1 + Profit %) = 200 / (1 + 25/100) = Rs.160.
Percentage Change
Example: A stock price increases from Rs.50 to Rs.60. What is the percentage increase?
We can use the formula for percentage change:
Percentage Increase = [(New Value – Old Value) / Old Value] x 100 = [(60 – 50) / 50] x 100 = 20%.
Practice Problems
To hone your percentage skills, try to solve the following problems:
- In an examination, a student scored 360 marks out of 500. What percentage did he score?
- A shopkeeper makes a profit of 20% by selling a book at Rs.120. What is the cost price of the book?
- If a person’s salary is decreased from Rs.5000 to Rs.4000, find the percentage decrease.
Summary
Percentage is a fundamental concept in quantitative aptitude, forming the base for numerous other topics. Its applications are extensive and varied, featuring prominently in areas like Profit & Loss, Simple & Compound Interest, and Data Interpretation. Aspirants should aim for a strong understanding of percentages and their application in different types of problems to score well in competitive exams. Remember that practicing different types of problems is the key to mastering this concept.