🔖 Percentages in Shopping Discounts
Irresistible offers? Thanks to the percentage! Easily calculate how much you'll save.
- 🛍️ S/200 with 25% discount → you pay S/150.
- 💥 “70% OFF” means a big discount off the original price.
Uses of Percentages
📊 Percentages in Finance and Economics
Percentages drive the world of money: interest, inflation, taxes... everything!
- 💰 8% interest on S/1000 → you earn S/80 per year.
- 📉 6% inflation reduces your purchasing power.
📈 Percentages in Statistics
Surveys? Data? Percentages tell stories without a thousand numbers.
- 📊 72% say “Yes” → 3 out of 4 agree.
- 🚬 18% smoke → social analysis in action.
🏫 Percentages in Education
Pass or fail? Percentages tell you if you made it.
- 📘 45 out of 50 points → 90% grade!
- 🎯 At least 70% required to pass a subject.
🩺 Percentages in Health
From body fat to medical effectiveness, percentages help take care of your health too!
- 💪 22% body fat: within the healthy range.
- 💊 Treatment effective in 85% of cases.
🧮 Percentages in Everyday Life
Percentages save you at the restaurant or in the kitchen—literally!
- 🍽️ 10% tip on S/150 → you leave S/15.
- 👨🍳 Cooking for 2 → cut the recipe by 50%.
Percentage Calculators
Simple Percentage Calculator
Easily calculate the percentage of a number, such as discounts and promotions.
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Percentage of a Total Calculator
This calculator helps you find the **total** when you know a part and its percentage. It's ideal for finding the original price of a discounted product or the full value of a quantity.
, then the total is:
Percentage of an Amount Calculator
This tool allows you to calculate **what percentage** a number represents of a total amount. It's perfect for determining the proportion of a value, such as a test grade or the discount on a product.
represents:
Percentage Change Calculator
This tool helps you **calculate an amount based on a percentage change**. It's useful for adjusting prices, evaluating increases or decreases in values, or quickly comparing ratios.
is:
How to Quickly Calculate Common Percentages in Your Head?
Master these simple mental math tricks to quickly calculate percentages. This is perfect for checking discounts while shopping, calculating a tip at a restaurant, or just improving your everyday math skills without a calculator.
🔵 50%
Half of any number!
Example: 50% of 80 = 80 ÷ 2 =
40
🟢 25%
One fourth!
Example: 25% of 80 = 80 ÷ 4 = 20
🟡 75%
Three fourths!
Example: 75% of 80 = (80 ÷ 4) × 3 =
60
🟠 10%
One tenth!
Example: 10% of 80 = 80 ÷ 10 = 8
🔴 20%
One fifth!
Example: 20% of 80 = 80 ÷ 5 = 16
Test Your Knowledge: Percentage Problems Quiz
Challenge yourself with these percentage problems. This quiz is designed to test your mental math skills and help you master common percentage calculations. After each question, you can check your answer and learn the solution.
If you get stuck, remember you can use our calculators for help. 👉 Jump to the Percentage Calculator
Solved Percentage Problems and Solutions by Difficulty Level
Master your percentage skills with our collection of solved exercises. We've organized problems by difficulty, from basic to expert, to help you learn and practice. Each exercise includes a clear, step-by-step solution.
Basic Level Exercises
These exercises cover fundamental percentage calculations, such as finding a percentage of a number or simple fractions.
| Exercise | Solution |
|---|---|
| 1. Calculate 50% of 200 | 50% of 200 = 200 × 0.50 = 100 |
| 2. Calculate 25% of 300 | 25% of 300 = 300 × 0.25 = 75 |
| 3. Calculate 75% of 400 | 75% of 400 = 400 × 0.75 = 300 |
| 4. Calculate 10% of 500 | 10% of 500 = 500 × 0.10 = 50 |
| 5. Calculate 20% of 150 | 20% of 150 = 150 × 0.20 = 30 |
Intermediate Level Exercises
These problems involve more complex calculations, like finding the original number or the percentage change between two values.
| Exercise | Solution |
|---|---|
| 6. Calculate 30% of 600 | 30% of 600 = 600 × 0.30 = 180 |
| 7. What percentage of 800 is 400? | 400 ÷ 800 × 100 = 50% |
| 8. Calculate 40% of 1,200 | 40% of 1,200 = 1,200 × 0.40 = 480 |
| 9. What percentage of 250 is 50? | 50 ÷ 250 × 100 = 20% |
| 10. Calculate 15% of 850 | 15% of 850 = 850 × 0.15 = 127.5 |
Advanced Level Exercises
Tackle real-world scenarios, including successive discounts, compound growth, and reverse percentage problems.
| Exercise | Solution |
|---|---|
| 11. An item costs $150 after a 20% discount. What was its original price? | Original price = $150 ÷ (1 - 0.20) = $187.50 |
| 12. An investment of $1,000 grows 12% in the first year and 15% in the second. What is the final value? | Final value = $1,000 × 1.12 × 1.15 = $1,288 |
| 13. A product increases by 25%, then decreases by 10%. What is the net percentage change? | Net change = (1 + 0.25) × (1 - 0.10) - 1 = 12.5% |
| 14. Calculate 5% of 9,000 | 5% of 9,000 = 9,000 × 0.05 = 450 |
| 15. If a price increases from $600 to $750, what is the percentage increase? | Percentage increase = (750 - 600) ÷ 600 × 100 = 25% |
Exercises with Solutions
Basic Exercise: Percentages
In a store, a pair of shoes costs $80 and is on sale with a 25% discount. What is the final price of the shoes after the discount?
| Original Price ($) | Discount (%) | Discounted Price ($) |
|---|---|---|
| 80 | 25 | x |
Solution:
- The discount is 25%, which means you pay 75% of the original price.
-
We calculate 75% of the original price:
Discounted Price Calculation \( \text{Final Price} = \text{Original Price} \times \frac{75}{100} \) \( = 80 \times \frac{75}{100} \) \( = 80 \times 0.75 = 60 \) - The discounted price is $60.
Answer: The final price of the shoes after the discount is $60.
Basic Exercise: Percentages
A student scored 72 out of 100 on an exam. What percentage of the total score did the student achieve?
| Score Obtained | Total Score | Percentage (%) |
|---|---|---|
| 72 | 100 | x |
Solution:
- To find the percentage, we use the formula:
Percentage Formula \( \text{Percentage} = \frac{\text{Score Obtained}}{\text{Total Score}} \times 100 \) \( = \frac{72}{100} \times 100 \) \( = 72\% \) - The student achieved 72% of the total score.
Answer: The percentage of the total score that the student achieved is 72%.
Intermediate Exercise: Percentages
A company has increased its employees' salaries by 12%. If an employee's original salary was $2,500 per month, what will their new salary be after the increase?
| Original Salary ($) | Increase (%) | New Salary ($) |
|---|---|---|
| 2500 | 12 | x |
Solution:
- The 12% increase is calculated based on the original salary.
-
Calculate 12% of $2,500:
Calculation Formula \( \text{Increase} = 2500 \times \frac{12}{100} \) \( = 2500 \times 0.12 \) \( = 300 \) -
Add the increase to the original salary:
New Salary Formula \( \text{New Salary} = 2500 + 300 \) \( = 2800 \) - The new salary is $2,800.
Answer: The employee's new salary after the increase is $2,800.
Intermediate Exercise: Percentages
A product is on sale with a 20% discount, and its discounted price is $80. What was the original price of the product before the discount?
| Discounted Price ($) | Discount (%) | Original Price ($) |
|---|---|---|
| 80 | 20 | x |
Solution:
- The discounted price represents 80% of the original price (100% - 20%).
-
Set up the formula:
Formula for Original Price \( 80 = x \times \frac{80}{100} \) -
Solve for x:
Solving the Formula \( x = \frac{80 \times 100}{80} \) \( = 100 \) - The original price of the product was $100.
Answer: The original price of the product before the discount was $100.
Basic Exercise: Percentage Change
A book used to cost $50 and now costs $60. What is the percentage increase in the price of the book?
| Concept | Value ($) |
|---|---|
| Original Price | 50 |
| New Price | 60 |
| Increase in Dollars | 10 |
| Increase (%) | x |
Solution:
-
Calculate the increase in dollars:
Increase = New Price - Original Price = 60 - 50 = 10 dollars -
Steps to calculate the percentage increase:
We use a simple proportion to find the percentage increase: -
Percentage Increase Calculation \( \frac{\text{Increase}}{\text{Original Price}} \times 100 \) \( = \frac{10}{50} \times 100 \) \( = 20\% \)
Answer: The percentage increase in the price of the book is 20%.
Intermediate Exercise: Sales Percentage Increase
A store reported that its sales in the first quarter of the year were $12,000. In the second quarter, sales increased to $15,500. What is the percentage increase in sales from one quarter to the next?
| First Quarter Sales ($) | Second Quarter Sales ($) | Increase (%) |
|---|---|---|
| 12,000 | 15,500 | x |
Solution:
- Calculate the increase in sales:
Sales Increase Calculation Increase = Second Quarter Sales - First Quarter Sales = 15,500 - 12,000 = 3,500 - Calculate the percentage increase:
Percentage Increase Calculation \( \frac{\text{Increase}}{\text{First Quarter Sales}} \times 100 \) \( = \frac{3,500}{12,000} \times 100 \) \( = 0.2917 \times 100 = 29.17\% \) - The percentage increase in sales is 29.17%.
Answer: The percentage increase in sales is 29.17%.
Intermediate Exercise: Cost Reduction Percentage
A company reduced the production cost of a product from $80 to $60 per unit. What is the percentage reduction in the production cost?
| Original Cost ($) | Reduced Cost ($) | Reduction (%) |
|---|---|---|
| 80 | 60 | x |
Solution:
- Calculate the cost reduction:
Cost Reduction Calculation Reduction = Original Cost - Reduced Cost = 80 - 60 = 20 - Calculate the percentage of reduction:
Percentage Reduction Calculation \( \frac{\text{Reduction}}{\text{Original Cost}} \times 100 \) \( = \frac{20}{80} \times 100 \) \( = 0.25 \times 100 = 25\% \) - The percentage reduction in the production cost is 25%.
Answer: The percentage reduction in the production cost is 25%.
Intermediate Exercise: Sales Share Percentage
A company has three products with the following sales in the last quarter: Product A with $5,000, Product B with $7,500, and Product C with $12,000. What percentage of the total sales does each product represent?
| Product | Sales ($) | Percentage (%) |
|---|---|---|
| Product A | 5,000 | x |
| Product B | 7,500 | x |
| Product C | 12,000 | x |
Solution:
- Calculate total sales:
Total Sales Calculation Total Sales = Product A + Product B + Product C = 5,000 + 7,500 + 12,000 = 24,500 - Calculate the sales share percentage for each product:
Sales Share Percentage Calculation \( \frac{\text{Product Sales}}{\text{Total Sales}} \times 100 \) Product A: \( \frac{5,000}{24,500} \times 100 = 20.41\% \) Product B: \( \frac{7,500}{24,500} \times 100 = 30.61\% \) Product C: \( \frac{12,000}{24,500} \times 100 = 48.98\% \) - Therefore, the sales share percentages are:
- Product A: 20.41%
- Product B: 30.61%
- Product C: 48.98%
Answer: The sales share percentage of each product is 20.41% for Product A, 30.61% for Product B, and 48.98% for Product C.
Intermediate Exercise: Profit Increase Percentage
A company reported profits of $50,000 in the first semester and $70,000 in the second semester. What percentage of the first semester's profit does the increase in profit represent?
| First Semester Profit ($) | Second Semester Profit ($) | Increase (%) |
|---|---|---|
| 50,000 | 70,000 | x |
Solution:
- Calculate the profit increase:
Profit Increase Calculation Increase = Second Semester Profit - First Semester Profit = 70,000 - 50,000 = 20,000 - Calculate the percentage increase relative to the first semester's profit:
Percentage Increase Calculation \( \frac{\text{Increase}}{\text{First Semester Profit}} \times 100 \) \( = \frac{20,000}{50,000} \times 100 \) \( = 0.40 \times 100 = 40\% \) - The percentage increase in profit is 40% compared to the first semester.
Answer: The profit increase in the second semester is 40% compared to the first semester.
Intermediate Exercise: Total Expense Percentage
A company has the following monthly expenses: Rent $2,000, Salaries $5,000, and Supplies $1,500. What percentage of the total expense does each type of expense represent?
| Expense | Amount ($) | Percentage (%) |
|---|---|---|
| Rent | 2,000 | x |
| Salaries | 5,000 | x |
| Supplies | 1,500 | x |
Solution:
- Calculate the total expense:
Total Expense Calculation Total Expense = Rent + Salaries + Supplies = 2,000 + 5,000 + 1,500 = 8,500 - Calculate the percentage that each expense represents:
Percentage Calculation for Each Expense Percentage = \( \frac{\text{Expense Amount}}{\text{Total Expense}} \times 100 \) Rent: \( \frac{2,000}{8,500} \times 100 \approx 23.53\% \) Salaries: \( \frac{5,000}{8,500} \times 100 \approx 58.82\% \) Supplies: \( \frac{1,500}{8,500} \times 100 \approx 17.65\% \) - Therefore, the percentages are:
- Rent: 23.53%
- Salaries: 58.82%
- Supplies: 17.65%
Answer: The percentage of each type of expense with respect to the total expense is 23.53% for Rent, 58.82% for Salaries, and 17.65% for Supplies.
Intermediate Exercise: Total Sales Percentage by Category
In a store, total sales for the month were $12,000. The sales by category were: Electronics $4,500, Clothing $3,200, and Furniture $2,300. What percentage of the total sales does each category represent?
| Category | Sales ($) | Percentage (%) |
|---|---|---|
| Electronics | 4,500 | x |
| Clothing | 3,200 | x |
| Furniture | 2,300 | x |
Solution:
- We calculate the percentage that each category represents:
Percentage Calculation for Each Category Percentage = \( \frac{\text{Category Sales}}{\text{Total Sales}} \times 100 \) Electronics: \( \frac{4,500}{12,000} \times 100 \approx 37.50\% \) Clothing: \( \frac{3,200}{12,000} \times 100 \approx 26.67\% \) Furniture: \( \frac{2,300}{12,000} \times 100 \approx 19.17\% \) - Therefore, the percentages are:
- Electronics: 37.50%
- Clothing: 26.67%
- Furniture: 19.17%
Answer: The percentage of sales for each category with respect to the total sales is 37.50% for Electronics, 26.67% for Clothing, and 19.17% for Furniture.
Intermediate Exercise: Percentage Increase
A book used to cost $40 and now costs $50. What is the percentage increase in the book's price?
| Previous Price ($) | Current Price ($) | Increase (%) |
|---|---|---|
| 40 | 50 | x |
Solution:
- We calculate the increase in price:
Increase Calculation Increase = Current Price - Previous Price = 50 - 40 = 10 - We calculate the percentage increase:
Percentage Increase Calculation Percentage Increase = \( \frac{\text{Increase}}{\text{Previous Price}} \times 100 \) = \( \frac{10}{40} \times 100 = 25\% \) - The percentage increase in the book's price is 25%.
Answer: The percentage increase in the book's price is 25%.
Intermediate Exercise: Discount Percentage
A television originally costs $600 and is on sale with a 15% discount. What is the final price of the television after the discount?
| Original Price ($) | Discount (%) | Discount Amount ($) | Final Price ($) |
|---|---|---|---|
| 600 | 15 | x | x |
Solution:
- We calculate the discount amount:
Discount Calculation Discount = Original Price \(\times \frac{Discount}{100}\) = 600 \(\times \frac{15}{100} = 600 \times 0.15 = 90\) - We calculate the final price after the discount:
Final Price Calculation Final Price = Original Price - Discount = 600 - 90 = 510 - The final price of the television after the discount is $510.
Answer: The final price of the television after the discount is $510.
Intermediate Exercise: Percentage Increase
An item used to cost $150 and its price increased by 20%. What is the new price of the item?
| Original Price ($) | Increase (%) | Increase Amount ($) | Final Price ($) |
|---|---|---|---|
| 150 | 20 | x | x |
Solution:
- We calculate the amount of the increase:
Increase Calculation Increase = Original Price \(\times \frac{Increase}{100}\) = 150 \(\times \frac{20}{100} = 150 \times 0.20 = 30\) - We calculate the final price after the increase:
Final Price Calculation Final Price = Original Price + Increase = 150 + 30 = 180 - The new price of the item after the increase is $180.
Answer: The new price of the item after the increase is $180.
Advanced Exercise: Survey Participation Percentage
In a survey with 800 participants, 35% chose option A, 25% chose option B, and 40% chose option C. How many participants chose each option?
| Option | Percentage (%) | Participants |
|---|---|---|
| Option A | 35 | x |
| Option B | 25 | x |
| Option C | 40 | x |
Solution:
- We calculate the number of participants for each option:
Calculation of Participants per Option Participants A = Total Participants \(\times \frac{Percentage A}{100}\) = 800 \(\times \frac{35}{100} = 800 \times 0.35 = 280\) Participants B = Total Participants \(\times \frac{Percentage B}{100}\) = 800 \(\times \frac{25}{100} = 800 \times 0.25 = 200\) Participants C = Total Participants \(\times \frac{Percentage C}{100}\) = 800 \(\times \frac{40}{100} = 800 \times 0.40 = 320\) - The number of participants for each option is:
- Option A: 280
- Option B: 200
- Option C: 320
Answer: The number of participants for each option is 280 for option A, 200 for option B, and 320 for option C.
Basic Exercise: Discount Percentage on a Purchase
A pair of shoes used to cost $120 and is now on sale with a 30% discount. What is the final price after the discount?
| Original Price ($) | Discount (%) | Discount ($) | Final Price ($) |
|---|---|---|---|
| 120 | 30 | x | x |
Solution:
- Calculate the discount amount:
Discount Calculation Discount = Original Price \(\times \frac{Discount}{100}\) = 120 \(\times \frac{30}{100} = 120 \times 0.30 = 36\) - Calculate the final price after the discount:
Final Price Calculation Final Price = Original Price - Discount = 120 - 36 = 84 - The final price of the shoes after the discount is $84.
Answer: The final price of the shoes after the discount is $84.
Intermediate Exercise: Sales Participation Percentage
In one month, a store sold 1,000 units of three different products: Product X (400 units), Product Y (300 units), and Product Z (300 units). What is the sales percentage for each product?
| Product | Units Sold | Percentage (%) |
|---|---|---|
| Product X | 400 | x |
| Product Y | 300 | x |
| Product Z | 300 | x |
Solution:
- Calculate the sales percentage for each product:
Sales Percentage Calculation Percentage X = \(\frac{Units\ Sold\ X}{Total\ Units} \times 100\) = \(\frac{400}{1000} \times 100 = 40\%\) Percentage Y = \(\frac{Units\ Sold\ Y}{Total\ Units} \times 100\) = \(\frac{300}{1000} \times 100 = 30\%\) Percentage Z = \(\frac{Units\ Sold\ Z}{Total\ Units} \times 100\) = \(\frac{300}{1000} \times 100 = 30\%\) - The sales percentages for each product are:
- Product X: 40%
- Product Y: 30%
- Product Z: 30%
Answer: The sales percentages are 40% for Product X, 30% for Product Y, and 30% for Product Z.
Advanced Exercise: Savings Percentage in a Purchase
A customer buys a laptop that originally cost $1,200, but a 25% discount is applied. How much does the customer save with the discount, and what is the final price of the laptop?
| Original Price ($) | Discount (%) | Savings ($) | Final Price ($) |
|---|---|---|---|
| 1200 | 25 | x | x |
Solution:
- We calculate the amount saved:
Savings Calculation Savings = Original Price \(\times \frac{Discount}{100}\) = 1200 \(\times \frac{25}{100} = 1200 \times 0.25 = 300\) - We calculate the final price after the discount:
Final Price Calculation Final Price = Original Price - Savings = 1200 - 300 = 900 - The customer saves $300 and the final price of the laptop is $900.
Answer: The customer saves $300 with the discount and the final price of the laptop is $900.
Advanced Exercise 1: Salary Increase
An employee received a 12% salary increase on their current salary of $3,500. After one year, the salary increases again by 8% on the new salary. What is the final salary after both increases?
| Initial Salary ($) | First Increase (%) | Salary After First Increase ($) | Second Increase (%) | Final Salary ($) |
|---|---|---|---|---|
| 3500 | 12 | x | 8 | x |
Solution:
- We calculate the salary after the first increase:
First Increase Calculation Salary After First Increase = Initial Salary \(\times \frac{First\ Increase}{100}\) = 3500 \(\times \frac{12}{100} = 3500 \times 0.12 = 420\) Salary After First Increase = Initial Salary + Increase = 3500 + 420 = 3920 - We calculate the salary after the second increase:
Second Increase Calculation Increase = Salary After First Increase \(\times \frac{Second\ Increase}{100}\) = 3920 \(\times \frac{8}{100} = 3920 \times 0.08 = 313.60\) Final Salary = Salary After First Increase + Increase = 3920 + 313.60 = 4233.60 - The final salary after both increases is $4,233.60.
Answer: The final salary after both increases is $4,233.60.
Advanced Exercise 2: Price Increase and Applied Discounts
A store increased the price of an item by 20% over the original price of $150. Later, a 15% discount was applied to the new price. What is the final price of the item after the increase and the discount?
| Original Price ($) | Increase (%) | Price After Increase ($) | Discount (%) | Final Price ($) |
|---|---|---|---|---|
| 150 | 20 | x | 15 | x |
Solution:
- We calculate the price after the increase:
Increase Calculation Increase = Original Price \(\times \frac{Increase}{100}\) = 150 \(\times \frac{20}{100} = 150 \times 0.20 = 30\) Price After Increase = Original Price + Increase = 150 + 30 = 180 - We calculate the final price after the discount:
Discount Calculation Discount = Price After Increase \(\times \frac{Discount}{100}\) = 180 \(\times \frac{15}{100} = 180 \times 0.15 = 27\) Final Price = Price After Increase - Discount = 180 - 27 = 153 - The final price of the item after the increase and the discount is $153.
Answer: The final price of the item after the increase and the discount is $153.
Advanced Exercise 3: Net Profit After Taxes
A company reports a gross profit of $50,000. After applying a 25% tax, the company decides to reinvest 10% of the net profit into new projects. What is the reinvested amount and what is the final net profit after taxes and reinvestment?
| Gross Profit ($) | Tax (%) | Net Profit After Taxes ($) | Reinvestment (%) | Reinvested Amount ($) | Final Net Profit ($) |
|---|---|---|---|---|---|
| 50000 | 25 | 37500 | 10 | 3750 | 33750 |
Solution:
- We calculate the net profit after taxes:
Net Profit Calculation Tax = Gross Profit \(\times \frac{Tax}{100}\) = 50000 \(\times \frac{25}{100} = 50000 \times 0.25 = 12500\) Net Profit After Taxes = Gross Profit - Tax = 50000 - 12500 = 37500 - We calculate the reinvested amount:
Reinvestment Calculation Reinvestment = Net Profit After Taxes \(\times \frac{Reinvestment}{100}\) = 37500 \(\times \frac{10}{100} = 37500 \times 0.10 = 3750\) Final Net Profit = Net Profit After Taxes - Reinvestment = 37500 - 3750 = 33750 - The reinvested amount is $3,750 and the final net profit after taxes and reinvestment is $33,750.
Answer: The reinvested amount is $3,750 and the final net profit after taxes and reinvestment is $33,750.