Questions and Answers
What is the result of a 20% decrease followed by a 10% increase on an original value of ₹500?
A shirt is sold at a 15% discount. If the selling price is ₹850, what is the original price?
If the population of a city increases by 10% every year, how much will it increase in 2 years?
A dealer buys a watch for ₹800 and sells it for ₹960. What is the profit percentage?
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If 25% of a number is 30, what is the number?
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A student scored 80 marks out of 100 in a test. What is the percentage score?
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A 25% increase in a quantity is equivalent to multiplying the original value by 1.25.
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The formula for calculating the new value after a decrease is New value = Original value + (Original value × Percentage decrease/100).
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If a shopkeeper sells an item at a 10% discount, then the selling price is 90% of the marked price.
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The profit percentage is always calculated on the selling price.
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The formula for calculating the profit percentage is Profit percentage = (Selling price - Cost price) / Selling price × 100.
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If a population decreases by 20% in one year and then increases by 20% in the next year, the population will remain the same.
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A simple interest of 10% per annum on a principal amount of ₹1000 for 2 years is ₹200.
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The compound interest on a principal amount of ₹1000 at a rate of 10% per annum for 2 years is more than the simple interest.
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The percentage change in a quantity is always calculated on the original value.
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Study Notes
Increasing and Decreasing Percentage
- Increase: addition of a certain percentage of the original value to itself
- Example: 25% increase in 100 = 100 + (25% of 100) = 100 + 25 = 125
- Decrease: subtraction of a certain percentage of the original value from itself
- Example: 25% decrease in 100 = 100 - (25% of 100) = 100 - 25 = 75
Percentage Change
- Percentage change = (change/original value) × 100
- Example: If the price of a shirt increases from ₹100 to ₹120, the percentage change = ((120-100)/100) × 100 = 20%
Percentage Formulas
- Percentage = (part/whole) × 100
- Part = (percentage/100) × whole
- Whole = (100/percentage) × part
Profit and Loss Percentage
- Profit percentage = (profit/original cost) × 100
- Loss percentage = (loss/original cost) × 100
- Selling price = cost price + profit (in case of profit)
- Selling price = cost price - loss (in case of loss)
Applications of Percentage
- Interest rates and investments
- Discounts and sales
- Population growth and decline
- Marks and grades in exams
- Increase or decrease in prices of goods and services
Understanding Percentage
- Increase in value is the addition of a certain percentage of the original value to itself
- Decrease in value is the subtraction of a certain percentage of the original value from itself
Calculating Percentage Change
- Formula: percentage change = (change/original value) × 100
- Example: price increase from ₹100 to ₹120 = 20% ((120-100)/100) × 100
Essential Percentage Formulas
- Percentage = (part/whole) × 100
- Part = (percentage/100) × whole
- Whole = (100/percentage) × part
Profit and Loss Percentage
- Profit percentage = (profit/original cost) × 100
- Loss percentage = (loss/original cost) × 100
- Selling price calculation: cost price + profit (in case of profit), or cost price - loss (in case of loss)
Real-World Applications of Percentage
- Interest rates and investments
- Discounts and sales
- Population growth and decline
- Marks and grades in exams
- Price changes in goods and services
Percentage for Class 8
Increasing and Decreasing Percentage
- To increase a quantity, multiply the original value by the percentage increase, then add it to the original value.
- Formula: New value = Original value + (Original value × Percentage increase/100)
- To decrease a quantity, multiply the original value by the percentage decrease, then subtract it from the original value.
- Formula: New value = Original value - (Original value × Percentage decrease/100)
- Always calculate percentage increase or decrease on the original value.
Profit and Loss Percentage
- Profit is the amount gained, and is calculated as a percentage of the cost price.
- Formula: Profit percentage = (Profit/Cost price) × 100
- Loss is the amount lost, and is calculated as a percentage of the cost price.
- Formula: Loss percentage = (Loss/Cost price) × 100
- Marked price is the price at which an item is marked for sale.
- Selling price is the price at which an item is sold.
- Discount is the amount by which the marked price is reduced.
- Always calculate profit or loss as a percentage of the cost price.
Applications of Percentage
- Discounts: Calculate the amount of discount and the selling price of an item.
- Interest: Calculate simple interest and compound interest on a principal amount.
- Population growth: Calculate the percentage increase or decrease in population over time.
- Marks and grades: Calculate the percentage of marks obtained in an exam and the corresponding grade.
- Real-life scenarios: Percentage is used in various areas, including sales and purchases, investments, banking, and finance.
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Description
Quiz on percentage increase, decrease, and percentage change concepts with examples
