PERCENTAGE PROBLEM & SOLUTION -
Example.1) Calculating a Percentage Increase Suppose you bought a stock at $50, and its value increased to $75. What is the percentage increase?
Ans.)
1. Calculate the increase: $75 - $50 = $25.
2. Use the formula for percentage increase:-
Percentage Increase = (Increase / Original Value) * 100
Percentage Increase = ($25 / $50) * 100 = 0.5 * 100 = 50%. (Ans.)
Example.2) Calculating a Percentage Decrease You had $200 in your bank account, and you spent $40. What is the percentage decrease in your account balance?
Ans.)
1. Calculate the decrease: $200 - $40 = $160.
2. Use the formula for percentage decrease:-
Percentage Decrease = (Decrease / Original Value) * 100
Percentage Decrease = ($160 / $200) * 100 = 0.8 * 100 = 80%. (Ans.)
Example.3) Finding a Part of a Whole You need to calculate 20% of 300 apples for a recipe. How many apples is that?
Ans.)
= 0.2 * 300 = 60 (Ans.)
Example.4) Applying Discounts You have a $100 item that's on sale for 25% off. How much will you pay after the discount?
Ans.)
Example.5) Expressing Fractions as Percentages You want to express the fraction 3/4 as a percentage.
Ans.)
Example.6) Percentage Change from Old to New If a city's population was 500,000 and increased to 600,000, what is the percentage change?
Ans.)
1. Calculate the change: 600,000 - 500,000 = 100,000.
2. Use the formula for percentage change:-
Percentage Change = (Change / Old Value) * 100 Percentage Change
= (100,000 / 500,000) * 100
= 0.2 * 100 = 20%. (Ans.)
Calculating a Percentage Increase:-
Example.7) The price of a product increased from $50 to $70. What is the percentage increase?
Ans.) Use the formula for percentage increase:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
In this case:
Percentage Increase = (($70 - $50) / $50) * 100
= ($20 / $50) * 100 = 40%. (Ans.)
Finding a Percentage of a Whole:-
Example.8) 30 out of 75 students passed a test. What percentage of students passed?
Ans.) Use the formula for finding a percentage of a whole:
Percentage = (Part / Whole) * 100
In this case:
Percentage = (30 / 75) * 100 = 40%. (Ans.)
Calculating a Percentage Decrease:-
Example.9) The temperature dropped from 80°F to 60°F. What is the percentage decrease?
Ans.) Use the formula for percentage decrease:
Percentage Decrease = ((Old Value - New Value) / Old Value) * 100
In this case:
Percentage Decrease = ((80 - 60) / 80) * 100
= (20 / 80) * = 25% (Ans.)
Finding Original Value After a Percentage Increase:-
Example.10) After a 15% increase, the new price of a product is $115. What was the original price?
Ans.) Use the formula to find the original value after a percentage increase:
Old Value = New Value / (1 + Percentage Increase)
In this case:
Old Value = $115 / (1 + 0.15) = $100 (Ans.)
Example.11) Calculating a Percentage Increase Problem: If the price of a product increased from $50 to $70, what is the percentage increase?
Ans.) Using the formula for percentage increase:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
Percentage Increase = (($70 - $50) / $50) * 100
= 0.4 * 100 = 40% (Ans.)
Calculating a Percentage Decrease Problem:-
Example.12) If the temperature decreased from 80°F to 60°F, what is the percentage decrease?
Ans.) Using the formula for percentage decrease:
Percentage Decrease = ((Old Value - New Value) / Old Value) * 100
Percentage Decrease = ((80 - 60) / 80) * 100
= 0.25 * 100 = 25% (Ans.)
Finding a Part of a Whole Problem:-
Example.13) If 30 out of 50 students in a class scored A grades, what percentage of the class scored A grades?
Ans.) Using the formula for expressing a part as a percentage of a whole:
Percentage = (Part / Whole) * 100
Percentage = (30 / 50) * 100 = 0.6 * 100 = 60% (Ans.)
Calculating Discounts Problem:-
Example.14) If a $100 item is on sale for $80, what is the percentage discount?
Ans.) Using the formula for percentage decrease:
Percentage Discount = ((Regular Price - Sale Price) / Regular Price) * 100
Percentage Discount = (($100 - $80) / $100) * 100
= 0.2 * 100 = 20% (Ans.)
Calculating Percentage of a Whole Quantity Problem:-
Example.15) In a basket of 40 apples, 12 are green. What percentage of the apples are green?
Ans.) Using the formula for expressing a part as a percentage of a whole:
Percentage = (Part / Whole) * 100
Percentage = (12 / 40) * 100 = 0.3 * 100 = 30% (Ans.)
These are just a few examples of percentage problems and their solutions. Percentages are widely used in various scenarios, and the concepts can be applied to a wide range of situations involving fractions of a whole. If you have specific problems you'd like assistance with, feel free to provide the details!