Aptitude Made Easy – Problems on Percentages full series, Learn maths #StayHome

Summary

This video script delves into the fundamentals of percentages, essential for aptitude exams. It covers basic concepts, such as converting fractions to percentages and vice versa, and memorizing common fractions' percentage equivalents for quick problem-solving. The script also addresses three common percentage problems: finding what percentage one number is of another, calculating increases or decreases in values, and understanding salary-related percentage questions. Additionally, it introduces advanced topics like expenditure rates, percentage changes in values, and area calculations for rectangles, providing formulas and examples to simplify the understanding of these concepts.

Takeaways

• 😀 Percentages are essentially per hundred, with the denominator always being 100.
• 📚 Understanding basic percentage concepts is crucial for solving problems involving percentages.
• 🔢 Converting percentages to fractions involves dividing by 100, and vice versa involves multiplying by 100.
• 💡 Memorizing fractions from 1/1 to 1/10 and their corresponding percentages can simplify solving aptitude test problems.
• 💼 Percentage problems often involve calculating a certain percentage of a given number, such as 33.33% of 180.
• 📈 When a value is increased by a certain percentage, the new value can be found by multiplying the original value by the factor representing the percentage increase.
• 📉 Similarly, when a value is decreased by a certain percentage, the new value is calculated by subtracting the percentage fraction from 1 and multiplying by the original value.
• 💼 Salary problems in aptitude exams often involve calculating what percentage one salary is less or more than another.
• 🛒 Expenditure problems typically involve calculating how changes in rate or consumption affect the total expenditure.
• 📦 The formula for calculating the overall change in value when multiple factors are increased or decreased is (A + B + AB/100), where A and B are the percentages of change.

Q & A

What does the term 'percentage' mean?

The term 'percentage' means 'per hundred', with the denominator always being 100 in any percentage calculation.

How do you convert a percentage to a fraction?

To convert a percentage to a fraction, you divide the percentage by 100. For example, 20% becomes 20 divided by 100, which simplifies to 1/5.

What is the fraction equivalent of 20%?

The fraction equivalent of 20% is 1/5.

How do you convert a fraction to a percentage?

To convert a fraction to a percentage, you multiply the fraction by 100. For instance, 1/5 becomes 20% when multiplied by 100.

What is the percentage of 3 out of 60?

The percentage of 3 out of 60 is 5%, as 3 divided by 60 equals 0.05, and when multiplied by 100 gives 5%.

Why is it beneficial to memorize the fractions from 1/1 to 1/10 in terms of percentages?

Memorizing these fractions and their corresponding percentages allows for quick calculations in aptitude exams, saving time and effort.

What is the result of 33.33% of 180?

33.33% of 180 is 60, because 33.33% is equivalent to 1/3, and 1/3 of 180 is 60.

How can you find out what percentage one number is of another without using the elaborate method?

If you know the fractions and their corresponding percentages by heart, you can directly calculate the percentage by using the fraction equivalent to the percentage you need to find.

What is the new value of X if X is increased by 20%?

If X is increased by 20%, the new value of X is 120% of the original X, or 1.2 times X.

How do you calculate the percentage decrease when a value is reduced by a certain percentage?

To calculate the percentage decrease, you subtract the percentage decrease from 100% and then apply this to the original value. For example, if X is decreased by 20%, the new value is 80% of X, or 0.8 times X.

What is the basic formula for calculating expenditure in terms of rate and consumption?

The basic formula for calculating expenditure is Expenditure = Rate × Consumption.

If the rate of a commodity increases by 50%, by what percentage must consumption decrease to keep the expenditure constant?

If the rate increases by 50%, consumption must decrease by 33.33% to keep the expenditure constant.

How can you find what percentage one number is of another when both are related to a third number by different percentage increases?

Assume the third number as 100, calculate the other two numbers based on their percentage increases, and then find the percentage of one number in relation to the other.

What is the formula to calculate the overall percentage change when two values are increased by different percentages?

The formula to calculate the overall percentage change when two values are increased by percentages a and b is (a + b + (a × b) / 100).

If the length of a rectangle is increased by 10% and the breadth by 20%, what is the overall percentage change in the area?

The overall percentage change in the area of the rectangle is 32%, using the formula for overall percentage change when two values are increased by different percentages.