# CLASS-6PERCENTAGE - 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.)

1. 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.)

1. Calculate the discount: \$100 * 0.25 = \$25.
2. 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.)

1. Convert the fraction to a decimal: 3/4 = 0.75.
2. 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!