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General Aptitude | Percentages | All Branches | GATE 2027 Quantitative Aptitude Preparation
GATE Wallah (English)
Overview
This video introduces the concept of percentages, explaining its fundamental definition and its crucial role in comparing fractions and solving various quantitative aptitude problems. It covers how to convert percentages to fractions and decimals, and emphasizes the importance of understanding these conversions for calculations. The session delves into successive percentage increases and decreases, demonstrating logical approaches to solve these problems without solely relying on formulas. It also touches upon percentage comparison and error percentage, providing practical examples and practice questions for the GATE exam.
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Chapters
- Percentages are a way to express a fraction out of 100, providing a standardized platform for comparison.
- Understanding percentages is foundational for advanced topics like profit and loss, simple interest, and compound interest.
- The core idea of percentage is 'per hundred' or 'out of 100'.
- Percentages are essential for comparing fractions, similar to how decimals or finding a common denominator (LCM) allows for comparison.
Grasping the fundamental concept of percentages is crucial as it forms the basis for many other quantitative aptitude topics and enables effective comparison of different values.
Comparing 1/2 and 1/3 by converting them to percentages (50% and 33.33%) to easily determine that 1/2 is greater.
- To convert a percentage to a fraction, divide the percentage value by 100 and simplify.
- To convert a percentage to a decimal, divide the percentage value by 100 (or move the decimal point two places to the left).
- It's beneficial to practice converting common percentages (e.g., 5%, 10%, 25%) to their fractional and decimal equivalents without a calculator to build intuition.
- Special attention should be paid to mixed percentages like 33 1/3% (1/3) and 66 2/3% (2/3) and their decimal representations (0.333... and 0.666...).
- Calculations may involve percentages greater than 100%, which can be handled by adding the percentage to 100% or converting directly.
Proficiency in converting between percentages, fractions, and decimals allows for quicker and more accurate calculations, especially in complex problems.
Writing down the conversions for every 5% increment from 5% to 100%, noting that 5% is 1/20 or 0.05, 10% is 1/10 or 0.1, and so on.
- Successive discounts or increases are not simply added together; the second change applies to the result of the first change.
- A logical approach involves starting with a base value (e.g., 100) or using the multiplier method (e.g., for a 10% increase, multiply by 1.10; for a 20% decrease, multiply by 0.80).
- When dealing with successive changes, multiply the resulting values (as decimals or percentages of the original). If the final value is less than 1 (or 100%), it indicates a net decrease; if it's greater than 1, it indicates a net increase.
- The change is calculated as the difference from 1 (for decimals) or 100% (for percentages), indicating the overall percentage increase or decrease.
This method provides a robust way to calculate the net effect of multiple percentage changes, preventing common errors like simple addition of percentages.
A product with a 50% discount followed by another 50% discount does not result in a 100% discount but a 75% discount (100 * 0.50 * 0.50 = 25, meaning a 75% decrease from the original 100).
- Percentage comparison is used when one quantity is a certain percentage more or less than another.
- If quantity A is X% more than quantity B, then B is less than A by a specific percentage that is not simply X%.
- The formula for percentage increase/decrease or error is (Difference / Actual Value) * 100.
- In problems involving constant products (like budget = rate * consumption or area = length * breadth), if one factor changes by a certain ratio, the other factor must change by the reciprocal ratio to maintain the product.
- When comparing quantities, it's essential to identify the base (the 'of' or 'than' value) upon which the percentage is calculated.
Understanding percentage comparison and its application in scenarios like maintaining a budget or constant area helps in solving real-world problems and advanced aptitude questions.
If petrol price increases by 40%, consumption must decrease by approximately 28.57% (calculated as 1 - (1 / 1.40)) to keep the total expenditure the same.
Key takeaways
- Percentages are a universal language for comparison, built on the foundation of 'out of 100'.
- Mastering the conversion between percentages, fractions, and decimals is fundamental for efficient problem-solving.
- Successive percentage changes require careful calculation; never simply add or subtract percentages directly.
- The multiplier method (e.g., 1.10 for a 10% increase, 0.80 for a 20% decrease) is a powerful tool for successive changes.
- When a product of two quantities is constant, changes in one quantity are inversely related to changes in the other.
- Always identify the base value when calculating percentages to avoid errors in comparison.
- Logical reasoning and understanding the underlying concepts are more valuable than memorizing formulas for aptitude tests.
Key terms
PercentageFractionDecimalSuccessive IncreaseSuccessive DecreaseBase ValueActual ValueError PercentComparison of Percentage
Test your understanding
- What is the primary advantage of using percentages for comparison?
- How does the calculation of successive percentage changes differ from simple addition of percentages?
- Explain the multiplier method for calculating successive percentage increases and decreases.
- If the price of an item increases by 25%, by what percentage must its consumption decrease to keep the total expenditure the same?
- What is the formula for calculating percentage increase or decrease, and what does the 'actual value' represent in this formula?