TLDR;
This YouTube video by SSC MAKER provides a comprehensive introduction to percentages, starting from the basics and gradually progressing to more complex problem-solving techniques. The video aims to build a strong foundation in percentage calculations, essential for various competitive exams.
- Introduces the concept of percentage and its representation.
- Explains how to convert percentages to fractions and vice versa.
- Covers methods to calculate percentage increase and decrease.
- Discusses application of percentages in population-based problems and income-expenditure scenarios.
- Provides short tricks and formulas for quick problem-solving.
Introduction to Percentages [0:02]
The video begins with a welcome and an overview of the class, emphasising a basic approach suitable for students with varying levels of understanding. The instructor aims to teach from a zero level, assuming no prior knowledge. The class will cover the concept of percentage, how to calculate it, and its applications. Students are encouraged to take notes.
Understanding the Basics of Percentage [0:55]
The lesson starts by defining percentage as a fraction where the denominator is always 100. The term 'percent' is explained as 'per' (out of) and 'cent' (hundred). The percentage symbol (%) is introduced. Examples are given to illustrate how to express percentages as fractions, such as 5% being equal to 5/100 and 10% being equal to 10/100. The importance of understanding this basic concept for solving arithmetic problems is highlighted.
Converting Percentages to Ordinary Fractions [6:34]
This section focuses on converting percentages into ordinary fractions (simple fractions). Examples include converting 5% to 1/20, 20% to 1/5, and 10% to 1/10. The process involves expressing the percentage as a fraction with a denominator of 100 and then simplifying the fraction to its simplest form.
Converting Fractions to Percentages [8:51]
The video explains how to convert a fraction into a percentage by multiplying the fraction by 100. Examples include converting 1/5 to 20%, 2/5 to 40%, and 1/10 to 10%. The instructor emphasises the simplicity of this method.
Converting Percentages to Decimals [11:52]
The method to convert percentages into decimal form is explained. For example, 35% is shown to be equivalent to 0.35, 60% to 0.60, and 95% to 0.95. The simple trick of moving the decimal point two places to the left is explained.
Calculating Percentage Values of Amounts [14:11]
This section teaches how to calculate the percentage value of a given amount. Examples include finding 20% of ₹60 (which is ₹12), 40% of 20 metres (which is 8 metres), and 15% of 700 (which is 105). The word 'of' is interpreted as multiplication. A special case is highlighted: x% of 100 is always x.
Percentage Calculation in Practical Scenarios [19:26]
The video demonstrates how to apply percentage calculations in practical scenarios. For example, calculating the percentage of marks obtained by a student in an exam. If a student scores 350 out of 500, the percentage is calculated as (350/500) * 100 = 70%.
Percentage Increase and Decrease [27:01]
This segment covers percentage increase and decrease. An example is given where a salary increases from ₹600 to ₹936. The percentage increase is calculated as ((936-600)/600) * 100 = 56%. Similarly, a decrease in salary from ₹600 to ₹450 is calculated as ((600-450)/600) * 100 = 25%.
Advanced Percentage Problems [31:15]
The video tackles more complex percentage problems. For example, finding a number that is 10% more than 240 (which is 264) and finding a number that is 10% less than 240 (which is 216). A problem involving successive percentage changes is also presented: if a salary increases by 30% and then decreases, the overall percentage change is calculated.
Percentage Problems: Increase and Decrease [41:49]
The video transitions to the second class, focusing on exam-oriented questions. It starts with a problem where A's income is 20% less than B's income, and the task is to find how much percent B's income is more than A's. The basic method and a short trick formula are provided to solve this type of problem.
Practice Problem: Percentage Difference [48:32]
A practice problem is presented where A's income is 25% less than B's income, and the task is to find how much percent B's income is more than A's. The basic method and the short trick formula are applied to solve this problem.
Percentage Increase and Decrease: Advanced Problems [54:27]
The video covers problems related to percentage increase and decrease. It starts with a problem where A's income is 10% more than B's income, and the task is to find how much percent B's income is less than A's. The basic method and the short trick formula are applied to solve this problem.
Practice Problem: Percentage Decrease [1:00:18]
A practice problem is presented where A's income is 25% more than B's income, and the task is to find how much percent B's income is less than A's. The basic method and the short trick formula are applied to solve this problem.
Percentage Problems: Expenditure and Consumption [1:06:57]
The video covers problems related to expenditure and consumption. It starts with a problem where the price of sugar increases by 10%, and the task is to find how much percent the consumption should be decreased to keep the expenditure constant. The basic method and the short trick formula are applied to solve this problem.
Practice Problem: Expenditure and Consumption [1:20:33]
A practice problem is presented where the price of sugar increases by 20%, and the task is to find how much percent the consumption should be decreased to keep the expenditure constant. The basic method and the short trick formula are applied to solve this problem.
Percentage Problems: Expenditure and Consumption with Increased Spending [1:27:25]
The video covers problems related to expenditure and consumption with increased spending. It starts with a problem where the price of onion increases by 25%, and a person decides to increase the expenditure by only 15%. The task is to find the percentage decrease in consumption. The basic method and the short trick formula are applied to solve this problem.
Successive Percentage Changes [1:35:52]
The video covers problems related to successive percentage changes. It starts with a problem where the salary of a person is decreased by 40% and then increased by 40%. The task is to find the overall percentage change in salary. The basic method and the short trick formula are applied to solve this problem.
Successive Percentage Changes: Practice Problem [1:45:14]
A practice problem is presented where the price of an item is increased by 20% and then decreased by 20%. The task is to find the overall percentage change in price. The basic method and the short trick formula are applied to solve this problem.
Percentage Problems: Area of a Rectangle [1:52:29]
The video covers problems related to the area of a rectangle. It starts with a problem where the length and breadth of a rectangle are increased by 10% and 20% respectively. The task is to find the overall percentage change in area. The basic method and the short trick formula are applied to solve this problem.
Population-Based Problems [2:01:43]
The video transitions to the third class, focusing on population-based problems. It starts with a problem where the population of a city is increasing at a rate of 20% per annum, and the task is to find the population after 2 years. The basic method and the short trick formula are applied to solve this problem.
Population-Based Problems: Practice Problem [2:10:03]
A practice problem is presented where the population of a city is increasing at a rate of 10% per annum, and the task is to find the population after 3 years. The basic method and the short trick formula are applied to solve this problem.
Population-Based Problems: Decreasing Population [2:15:10]
The video covers problems related to decreasing population. It starts with a problem where the population of a city is decreasing at a rate of 10% per annum, and the task is to find the population after 3 years. The basic method and the short trick formula are applied to solve this problem.
Population-Based Problems: Finding Population Before [2:20:41]
The video covers problems related to finding the population before a certain period. It starts with a problem where the current population of a city is 12100, and the population is increasing at a rate of 10% per annum. The task is to find the population 2 years ago. The basic method and the short trick formula are applied to solve this problem.
Population-Based Problems: Finding Population Before - Practice [2:45:55]
A practice problem is presented where the current population of a city is 8100, and the population is decreasing at a rate of 10% per annum. The task is to find the population 2 years ago. The basic method and the short trick formula are applied to solve this problem.
Problems on Literacy and Population [2:48:24]
The video addresses problems related to literacy and population. It starts with a problem where 70% of the population of a city is literate, and the number of illiterate people is 93000. The task is to find the number of literate people. The basic method and the short trick formula are applied to solve this problem.
Income and Expenditure Problems [2:53:28]
The video transitions to problems related to income and expenditure. It starts with a problem where a person spends 20% of his income on orphanage and 25% on school fees, and saves ₹4500. The task is to find his monthly income. The basic method and the short trick formula are applied to solve this problem.
Income, Expenditure, and Savings Problems [3:05:09]
The video covers problems related to income, expenditure, and savings. It starts with a problem where a person spends 50% of his income on his son and 30% on his daughter, and then donates 80% of the remaining amount to a trust. If he is left with ₹16000, the task is to find his initial income. The basic method and the short trick formula are applied to solve this problem.
EMI Calculation and Percentage of Monthly Income [3:14:27]
The video covers problems related to EMI calculation and percentage of monthly income. It starts with a problem where a person's annual income is ₹24 lakh, and he pays an EMI of ₹40000 per month. The task is to find the percentage of his monthly income that is spent on EMI. The basic method and the short trick formula are applied to solve this problem.
Income and Expenditure Problems: Advanced [3:10:12]
The video transitions to the fourth class, focusing on more advanced income and expenditure problems. It starts with a problem where a person spends 50% of his income on food and 20% on rent, and saves ₹1500. The task is to find his monthly income. The basic method and the short trick formula are applied to solve this problem.
Income and Expenditure Problems with Remaining Amount [3:16:34]
The video covers problems related to income and expenditure with the remaining amount. It starts with a problem where a person spends 15% of his income on rent and 60% of the remaining amount on household expenses, and saves ₹2210. The task is to find his monthly income. The basic method and the short trick formula are applied to solve this problem.
Income and Expenditure Problems: Advanced Practice [3:25:33]
A practice problem is presented where a person spends 30% of her income on rent and 60% of the remaining amount on household expenses, and saves ₹6300. The task is to find her monthly income. The basic method and the short trick formula are applied to solve this problem.
Election-Based Problems: Introduction [3:33:53]
The video transitions to election-based problems. It starts with a problem where there are two candidates in an election, and the winning candidate gets 60% of the votes and wins by 140000 votes. The task is to find the number of votes received by the winning candidate, the number of votes received by the losing candidate, and the total number of votes. The basic method and the short trick formula are applied to solve this problem.
Election-Based Problems: Practice Problem [3:48:20]
A practice problem is presented where there are two candidates in an election, and the winning candidate gets 55% of the votes and wins by 45000 votes. The task is to find the total number of votes. The basic method and the short trick formula are applied to solve this problem.
Election-Based Problems: With Invalid Votes [3:53:29]
The video covers election-based problems with invalid votes. It starts with a problem where there are two candidates in an election, 10% of the voters did not cast their votes, and the winning candidate gets 60% of the total votes and wins by 90000 votes. The task is to find the total number of votes. The basic method and the short trick formula are applied to solve this problem.
Election-Based Problems: With Invalid Votes and Percentage of Cast Votes [4:05:09]
The video covers election-based problems with invalid votes and percentage of cast votes. It starts with a problem where there are two candidates in an election, 10% of the voters did not cast their votes, and the winning candidate gets 60% of the cast votes and wins by 72000 votes. The task is to find the total number of votes. The basic method and the short trick formula are applied to solve this problem.
Pass/Fail Related Problems [4:26:38]
The video transitions to the fifth class, focusing on pass/fail related problems. It starts with a problem where the passing percentage in an exam is 40%, and a student scores 233 marks and fails by 17 marks. The task is to find the total marks of the exam. The basic method and the short trick formula are applied to solve this problem.
Finding Percentage of Marks [4:38:14]
The video covers problems related to finding the percentage of marks. It starts with a problem where a student scores 312 marks in an exam, which is 52% of the total marks. Another student scores 366 marks. The task is to find the percentage of marks scored by the second student. The basic method and the short trick formula are applied to solve this problem.
Finding Total Marks [4:41:03]
The video covers problems related to finding the total marks. It starts with a problem where a student scores 260 marks in an exam, which is 52% of the total marks. Another student scores 76%. The task is to find the marks scored by the second student. The basic method and the short trick formula are applied to solve this problem.
Finding Total Marks with Pass Marks [4:45:06]
The video covers problems related to finding the total marks with pass marks. It starts with a problem where a student scores 52% marks and gets 48 marks more than the pass marks. Another student scores 35% marks and gets 20 marks less than the pass marks. The task is to find the total marks of the exam. The basic method and the short trick formula are applied to solve this problem.
Mixture Problems [4:58:21]
The video transitions to mixture problems. It starts with a problem where there is a 240-gram solution of salt and water, and the solution contains 80% water. The task is to find how much water should be added to make the solution contain 95% water. The basic method and the short trick formula are applied to solve this problem.
Mixture Problems: Practice [5:25:02]
A practice problem is presented where there is a 40-litre mixture of milk and water, and the mixture contains 10% water. The task is to find how much water should be added to make the mixture contain 20% water. The basic method and the short trick formula are applied to solve this problem.
Mixture Problems: Adding Salt [5:29:03]
The video covers mixture problems where salt is added. It starts with a problem where there is a 480-gram solution of salt and water, and the solution contains 90% water. The task is to find how much salt should be added to make the solution contain 20% salt. The basic method and the short trick formula are applied to solve this problem.
Mixture Problems: Removing Water [5:35:04]
The video covers mixture problems where water is removed. It starts with a problem where there is a 600-gram solution of sugar and water, and the solution contains 5% sugar. The task is to find how much water should be evaporated to make the solution contain 80% water. The basic method and the short trick formula are applied to solve this problem.
Miscellaneous Problems: Ratio and Percentage [5:39:17]
The video transitions to the sixth class, focusing on miscellaneous problems. It starts with a problem where x is 22% and y is 30%. The task is to find the ratio of x to y. The basic method and the short trick formula are applied to solve this problem.
Ratio and Percentage Problems [5:42:12]
The video covers problems related to ratio and percentage. It starts with a problem where (p - q) is 50% and (p + q) is 30%. The task is to find the ratio of p to q. The basic method and the short trick formula are applied to solve this problem.
Percentage Calculation Problems [5:45:52]
The video covers problems related to percentage calculation. It starts with a problem where one-third of 1206 is what percentage of 134. The basic method and the short trick formula are applied to solve this problem.
Percentage Decrease Problems [5:48:27]
The video covers problems related to percentage decrease. It starts with a problem where when 25 is subtracted from a number, it becomes 80% of itself. The task is to find 40% of that number. The basic method and the short trick formula are applied to solve this problem.
Percentage Increase Problems [5:53:20]
The video covers problems related to percentage increase. It starts with a problem where when a number is increased by 24, it becomes 115% of itself. The task is to find the number. The basic method and the short trick formula are applied to solve this problem.
Income-Based Percentage Problems [6:01:21]
The video covers income-based percentage problems. It starts with a problem where Arun's income is 150% of Bala's income, and Chandu's income is 120% of Arun's income. If the total income of Arun, Bala, and Chandu is 86000, the task is to find Chandu's income. The basic method and the short trick formula are applied to solve this problem.
