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Download NowUnderstanding and calculating percentages are essential skills tested in the SSC CGL and other competitive exams. Percentages represent a fraction of 100 and are a fundamental way to express ratios, proportions, and comparisons in an easily understandable form.
Understanding Percentages
A percentage is a number or ratio expressed as a fraction of 100. It is denoted using the percent sign (%). For example, saying “50%” is numerically equivalent to or 0.5.
Key Percentage Formulas
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Calculating Percentage:
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Finding the Part:
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Finding the Whole:
Example Problems and Solutions
Problem 1: Basic Percentage Calculation
Question: If 25 out of 50 students in a class are boys, what percentage of the class is made up of boys?
Solution:
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Apply the Percentage Formula:
Conclusion: 50% of the class are boys.
Problem 2: Finding the Part Given the Percentage
Question: What is 20% of ₹500?
Solution:
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Use the formula to find the Part:
Conclusion: 20% of ₹500 is ₹100.
Problem 3: Determining the Whole from a Percentage
Question: If 25% of a number is 75, what is the number?
Solution:
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Rearrange the formula to find the Whole:
Conclusion: The original number is 300.
Problem 4: Percent Increase and Decrease
Question: A shopkeeper increases the price of a product from ₹200 to ₹250. What is the percentage increase?
Solution:
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Calculate the increase:
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Calculate the percentage increase:
Conclusion: The price was increased by 25%.
Strategies for Solving Percentage Problems
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Understand the Formulae: Make sure you are comfortable converting between parts, wholes, and percentages using the formulas.
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Practice Different Scenarios: Work through problems involving percentage increases, decreases, and conversions between fractions and percentages to build flexibility.
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Check Units and Terms: Ensure that you correctly interpret what the “whole” and the “part” refer to in word problems to avoid common mistakes.
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Use a Calculator Efficiently: While calculators can speed up calculations, ensure your setup of the problem is correct to avoid input errors.
Percentages are a versatile tool in mathematics, crucial for examinations and practical in everyday situations. Mastering percentage calculations can significantly enhance your data interpretation skills and help you excel in competitive exams like the SSC CGL.