If 120 Marks Is $60 \%$, What Are The Full Marks?

by ADMIN 52 views

Understanding the Problem

In this problem, we are given that 120 marks represent 60% of the total marks. We need to find the full marks, which is the total number of marks that represents 100%.

Breaking Down the Problem

To solve this problem, we can use the concept of percentages. We know that 60% of the total marks is equal to 120 marks. We can set up an equation to represent this:

60% of x = 120

where x is the total number of marks.

Converting Percentage to Decimal

To convert the percentage to a decimal, we can divide by 100:

60 ÷ 100 = 0.6

So, the equation becomes:

0.6x = 120

Solving for x

To solve for x, we can divide both sides of the equation by 0.6:

x = 120 ÷ 0.6

x = 200

Full Marks

Therefore, the full marks are 200.

Why is This Important?

Understanding how to calculate percentages and solve equations is an essential skill in mathematics. It has numerous applications in real-life situations, such as:

  • Calculating grades and scores
  • Determining the cost of items on sale
  • Understanding interest rates and investments
  • Analyzing data and statistics

Real-World Applications

Here are a few examples of how this concept is used in real-life situations:

  • Grading System: In a school, a student scores 60% on a test. If the test has 120 marks, what is the full marks?
  • Discounts: A store offers a 40% discount on a product. If the original price is $100, what is the discounted price?
  • Investments: A person invests $1000 in a stock that earns a 10% annual interest rate. How much will the person earn in interest after one year?

Tips and Tricks

Here are a few tips and tricks to help you solve similar problems:

  • Use a calculator: When working with percentages, it's often easier to use a calculator to convert the percentage to a decimal.
  • Check your units: Make sure you are using the correct units when solving the problem. In this case, we are working with marks, not dollars.
  • Read the problem carefully: Take your time to read the problem carefully and understand what is being asked.

Conclusion

In conclusion, if 120 marks is 60%, the full marks are 200. This problem requires an understanding of percentages and how to solve equations. It has numerous applications in real-life situations, such as calculating grades and scores, determining the cost of items on sale, and understanding interest rates and investments. By following the tips and tricks provided, you can solve similar problems with ease.

Frequently Asked Questions

Here are a few frequently asked questions related to this problem:

  • What is the full marks if 80% is 160 marks?
  • How do I calculate the percentage of a number?
  • What is the difference between a percentage and a decimal?

Answers

  • What is the full marks if 80% is 160 marks? The full marks are 200.
  • How do I calculate the percentage of a number? To calculate the percentage of a number, divide the number by 100 and multiply by the percentage.
  • What is the difference between a percentage and a decimal? A percentage is a number expressed as a fraction of 100, while a decimal is a number expressed as a fraction of 10.

Additional Resources

Here are a few additional resources that you can use to learn more about percentages and how to solve equations:

  • Online tutorials: Websites such as Khan Academy and Mathway offer interactive tutorials and exercises to help you learn.
  • Textbooks: Books such as "Algebra and Trigonometry" by Michael Sullivan and "Mathematics for Dummies" by Mary Jane Sterling provide comprehensive explanations and examples.
  • Practice problems: Websites such as IXL and Math Open Reference offer practice problems and quizzes to help you test your skills.
    Frequently Asked Questions: Percentages and Equations =====================================================

Q: What is the full marks if 80% is 160 marks?

A: To find the full marks, we can use the concept of percentages. We know that 80% of the total marks is equal to 160 marks. We can set up an equation to represent this:

80% of x = 160

where x is the total number of marks.

To solve for x, we can divide both sides of the equation by 0.8:

x = 160 ÷ 0.8

x = 200

Therefore, the full marks are 200.

Q: How do I calculate the percentage of a number?

A: To calculate the percentage of a number, you can use the following formula:

Percentage = (Number ÷ 100) × 100

For example, if you want to find 25% of 120, you can plug in the values as follows:

Percentage = (120 ÷ 100) × 100 = 1.2 × 100 = 120

Therefore, 25% of 120 is 120.

Q: What is the difference between a percentage and a decimal?

A: A percentage is a number expressed as a fraction of 100, while a decimal is a number expressed as a fraction of 10.

For example, 25% is equal to 0.25, which is a decimal.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you can divide the percentage by 100.

For example, to convert 25% to a decimal, you can divide 25 by 100:

25 ÷ 100 = 0.25

Therefore, 25% is equal to 0.25.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, you can multiply the decimal by 100.

For example, to convert 0.25 to a percentage, you can multiply 0.25 by 100:

0.25 × 100 = 25%

Therefore, 0.25 is equal to 25%.

Q: What is the formula for calculating the percentage increase?

A: The formula for calculating the percentage increase is:

Percentage Increase = ((New Value - Old Value) ÷ Old Value) × 100

For example, if the old value is 100 and the new value is 120, you can plug in the values as follows:

Percentage Increase = ((120 - 100) ÷ 100) × 100 = (20 ÷ 100) × 100 = 20%

Therefore, the percentage increase is 20%.

Q: What is the formula for calculating the percentage decrease?

A: The formula for calculating the percentage decrease is:

Percentage Decrease = ((Old Value - New Value) ÷ Old Value) × 100

For example, if the old value is 100 and the new value is 80, you can plug in the values as follows:

Percentage Decrease = ((100 - 80) ÷ 100) × 100 = (20 ÷ 100) × 100 = 20%

Therefore, the percentage decrease is 20%.

Q: How do I calculate the percentage of a mixed number?

A: To calculate the percentage of a mixed number, you can convert the mixed number to an improper fraction and then divide by 100.

For example, if you want to find 25% of 2 1/2, you can convert 2 1/2 to an improper fraction:

2 1/2 = 5/2

Then, you can multiply 5/2 by 25%:

(5/2) × (25/100) = (5 × 25) / (2 × 100) = 125/200 = 0.625

Therefore, 25% of 2 1/2 is 0.625.

Q: How do I calculate the percentage of a decimal?

A: To calculate the percentage of a decimal, you can multiply the decimal by 100.

For example, if you want to find 25% of 0.5, you can multiply 0.5 by 25%:

0.5 × (25/100) = 0.5 × 0.25 = 0.125

Therefore, 25% of 0.5 is 0.125.

Q: How do I calculate the percentage of a fraction?

A: To calculate the percentage of a fraction, you can convert the fraction to a decimal and then multiply by 100.

For example, if you want to find 25% of 1/2, you can convert 1/2 to a decimal:

1/2 = 0.5

Then, you can multiply 0.5 by 25%:

0.5 × (25/100) = 0.5 × 0.25 = 0.125

Therefore, 25% of 1/2 is 0.125.

Conclusion

In conclusion, percentages and equations are essential concepts in mathematics that have numerous applications in real-life situations. By understanding how to calculate percentages and solve equations, you can solve a wide range of problems and make informed decisions. We hope that this article has provided you with a comprehensive understanding of percentages and equations and has helped you to improve your math skills.