LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PERCENTAGE - PROBLEM & SOLUTION

__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.)**

**Calculate 20% of 300: 20% of 300 = (20 / 100) * 300**

** = 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.)**

**Calculate the discount: $100 * 0.25 = $25.****Subtract the discount from the original price: $100 - $25 = $75. (Ans.)**

**Example.5) Expressing Fractions as Percentages
You want to express the fraction 3/4 as a percentage.**

**Ans.)**

**Convert the fraction to a decimal: 3/4 = 0.75.****Convert the decimal to a percentage: 0.75 * 100 = 75%**.**(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:**

**Old Value = $50****New Value = $70**

**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:**

**Part (Students who passed) = 30****Whole (Total students) = 75**

**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:**

**Old Value = 80°F****New Value = 60°F**

**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:**

**New Value = $115****Percentage Increase = 15% or 0.15**

**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!**