Percentages | Introduction | Quantitative Aptitude | TalentSprint Aptitude Prep

Summary

This video provides an in-depth exploration of percentages, explaining their importance in quantitative aptitude and various related topics such as profit and loss, interest calculations, and data interpretation. The concept of percentage as a fraction with a denominator of 100 is introduced, followed by examples demonstrating its significance in comparing student performance, calculating profits, and simplifying complex problems. Key methods like converting percentages to fractions and vice versa, calculating percentage of a value, and cross-multiplication for quick solutions are discussed, making it an essential guide for mastering percentages in various mathematical contexts.

Takeaways

• 😀 Percentages are crucial in quantitative aptitude as they are the foundation for topics like profit and loss, simple interest, compound interest, and data interpretation.
• 😀 A percentage represents 'per 100', meaning a fraction where the denominator is always 100.
• 😀 When comparing two students' scores, it is important to use percentages instead of raw marks to make fair comparisons, as percentage normalizes performance across different exam scales.
• 😀 Percentage scores standardize the comparison by representing the marks obtained as a fraction of the total possible marks (out of 100).
• 😀 Profit and loss calculations are usually done using percentages to simplify understanding and comparison. For instance, a 20% profit means 20 rupees per every 100 invested.
• 😀 To convert a percentage into a fraction, divide the percentage by 100. Conversely, to convert a fraction into a percentage, multiply by 100.
• 😀 The formula to calculate a percentage value is: X percent of Y = (X * Y) / 100. This formula works for calculating profit, loss, or any percentage-related value.
• 😀 In percentage calculations, there are three key values: the percentage value, the maximum value, and the absolute value. One of these is given, and the others can be derived.
• 😀 Cross-multiplication can quickly help solve percentage problems. For example, to find what percent of a number is another number, cross-multiply the known values and solve.
• 😀 The relationship between percentages is symmetric: X percent of Y equals Y percent of X. This property can simplify calculations by switching the order of values.
• 😀 To increase or decrease a value by a percentage, the formula is: New Value = Original Value ± (Percentage * Original Value). Use '+' for increase and '-' for decrease.

Q & A

What does the symbol '%' mean in percentages?

The symbol '%' means 'per hundred' or 'out of every hundred'. It represents a fraction with a denominator of 100.

How is a percentage expressed as a fraction?

A percentage is expressed as a fraction by dividing the percentage value by 100. For example, 50% becomes 50/100, which simplifies to 1/2.

Why is percentage used to compare students' performance?

Percentage is used to compare students' performance because it provides a common scale for comparison, regardless of the maximum marks in their exams.

What is the relationship between percentages and fractions?

A percentage can be converted into a fraction by dividing the percentage by 100. Conversely, a fraction can be converted into a percentage by multiplying it by 100.

What is the formula for calculating 'X percent of Y'?

The formula for calculating X percent of Y is: (X/100) * Y, which simplifies to (X * Y) / 100.

How do you calculate the percentage if the actual value and the maximum value are given?

To calculate the percentage, use the formula: (Actual Value / Maximum Value) * 100. For example, if the actual value is 60 and the maximum value is 100, the percentage is (60/100) * 100 = 60%.

What is the method to convert a fraction into a percentage?

To convert a fraction into a percentage, multiply the fraction by 100. For example, 3/8 becomes (3/8) * 100 = 37.5%.

Can X percent of Y be equal to Y percent of X? If so, why?

Yes, X percent of Y is always equal to Y percent of X. This is because multiplication is commutative, meaning X * Y equals Y * X.

How do you calculate the new value when something is increased or decreased by a percentage?

To calculate the new value when a quantity is increased or decreased by a percentage, use the formula: New Value = Original Value ± (Percentage * Original Value). Use '+' for increase and '-' for decrease.

If a salary is 40,000 and it increases by 25%, what is the new salary?

The new salary is calculated as: 40,000 + (25% of 40,000) = 40,000 + 10,000 = 50,000.