Basic Word Problems on Percentage.

1. Percentage of a Quantity: Converting a percentage to a decimal and multiplying by the total.
2. Finding the Total from a Percentage: Setting up and solving an equation to find the total when given the percentage and part.
3. Percentage Increase: Calculating the difference, dividing by the original, and converting to a percentage.
4. Percentage Decrease: Similar to percentage increase but applied to decrease.
5. Finding the Percentage: Dividing the part by the total and converting to a percentage.

Problem1: A school has 500 students. If 60% of the students are boys, how many boys are there in the school?

Solution:

Convert the percentage to a decimal

60% = 60/100 = 0.60

Multiply the decimal by the total number of students

Number of boys = 0.60 × 500 = 300

Answer: There are 300 boys in the school.

Problem2: Sarah scored 45 marks in a test. This is 75% of the total marks. What are the total marks?

Solution:

Let the total marks be x.

75% of x is 45

(75/100)x = 45

0.75x= 45

Solve for x

Divide both sides by 0.75

0.75x/0.75 = 45/0.75

x = 45/0.75 = 60

Answer: The total marks are 60.

Problem3: The price of a book increased from $20 to $25. What is the percentage increase?

Solution:

Find the increase in price

Increase = 25 − 20 = 5

Calculate the percentage increase:

Percentage increase = 5/20 x 100

(5/20)×100 = 25

Percentage increase = 25%

Answer: The price increased by 25%.

Problem4: A car’s value decreased from $15,000 to $12,000. What is the percentage decrease?

Solution:

Find the decrease in value:

Decrease=15,000−12,000=3,000

Calculate the percentage decrease

Percentage decrease=(3,000/15,000)×100=20%

Answer: The car’s value decreased by 20%.

Problem5: After a 20% discount, a jacket costs $80. What was the original price?

Solution:

1. After a 20% discount, the jacket costs $80

Let the original price be x

Discount rate= 20%

Discount 20% of x = (x) x (20/100) = 0.2x

Sale price = Original Price – Discount

After a 20% discount

1. 80=x−0.20
   • 80=0.80x
2. Solve for x
   • Divide both sides by 0.80
   • x=80/0.80
   • =100

Answer: The original price of the jacket was $100.

Problem6: Out of 250 apples, 75 are rotten. What percentage of the apples are rotten?

Solution:

Calculate the percentage

Percentage of rotten apples=(75/250)×100=30%

Answer: 30% of the apples are rotten.

Problem7: A laptop was sold for $540 after a 10% increase in its original price. What was the original price?

Solution:

Let the original price be x

After a 10% increase, the selling price is $540

540=1.10x

1.10x=540

Solve for x

Divide both sides by 1.10

1.10x/1.10=540/1.10

x=540/1.10=490.91

Answer: The original price of the laptop was $490.91.

Problem8: A library has 800 books. If 25% of the books are fiction, how many fiction books are there in the library?

Solution:

Convert the percentage to a decimal

25%=25/100=0.25

Multiply the decimal by the total number of books

Number of fiction books=0.25×800=200

Answer: There are 200 fiction books in the library.

Problem9: John got 90 marks in his math exam, which is 75% of the total marks. What are the total marks?

Solution:

Let the total marks be x

75% of x is 90

0.75x=90

0.75x = 90

0.75x=90

Solve for x

Divide both sides by 0.75

x=90/0.75=120

Answer: The total marks are 120.

Problem10: The population of a town increased from 50,000 to 60,000. What is the percentage increase?

Solution:

Find the increase in population:

Increase=60,000−50,000=10,000

Calculate the percentage increase

Percentage increase=(10,000/50,000)×100

=20%

Answer: The population increased by 20%.

Problem11: After a 10% discount, a dress costs $54. What was the original price?

Solution:

Let the original price be x.

Discount rate= 10%

Discount 10% of x = (x) x (10/100) = 0.1x

Sale price = Original Price – Discount

After a 10%

x – 0.1x = 0.9x

the dress costs $54

54=x−0.10x

54 = 0.90x

Solve for x

Divide both sides by 0.90

x=54/0.90=60

x = 60

Answer: The original price of the dress was $60.

Problem12: Out of 500 employees, 125 are managers. What percentage of the employees are managers?

Solution:

Calculate the percentage

Percentage of managers=(125/500)×100

=25%

Answer: 25% of the employees are managers.

Problem13: A bicycle was sold for $270 after a 10% markup on its original price. What was the original price?

Solution:

1. Let the original price be x
   • After a 10% markup, the selling price is $270
   • 270=1.10x
   • 270 = 1.10x
   • 270=1.10x
2. Solve for x
   • Divide both sides by 1.10
   • x=270/1.10=245.45

Answer: The original price of the bicycle was $245.45.

Problem14: A class has 40 students. If 30% of the students are girls, how many girls are there in the class?

Solution:

Convert the percentage to a decimal 30%=30/100

=0.30

Multiply the decimal by the total number of students:

Number of girls=0.30×40=12

Answer: There are 12 girls in the class.

Problem15: Michael received $45, which is 75% of his weekly allowance. What is his total weekly allowance?

Solution:

1. Let the total weekly allowance be x
2. 75% of x is =45
3. Solve for x
   • Divide both sides by 0.75
   • x=45/0.75=60

Answer: Michael’s total weekly allowance is $60.

Problem16: The price of a movie ticket increased from $8 to $10. What is the percentage increase?

Solution:

Find the increase in price Increase=10−8=2

Calculate the percentage increase:

Percentage increase=2/8×100=25%

Answer: The price increased by 25%.

Problem17: A smartphone’s price dropped from $600 to $450. What is the percentage decrease?

Solution:

Find the decrease in price

Decrease=600−450=150

Calculate the percentage decrease

Percentage decrease=150/600×100

=25%

Answer: The price decreased by 25%.

Problem18: After a 15% discount, a jacket costs $85. What was the original price?

Solution:

1. Let the original price be x
   • After a 15% discount, the jacket costs $85
   • 85=x−0.15x
   • 85 = x – 0.15x
   • 85=x−0.15x
   • 85=0.85x
2. Solve for :
   • Divide both sides by 0.85
   • x=85/0.85=100

Answer: The original price of the jacket was $100.

Problem19: Out of 1200 students, 300 are in the science club. What percentage of the students are in the science club?

Solution:

Calculate the percentage:

Percentage of students in the science club

=(300/1200)×100

=25%

Answer: 25% of the students are in the science club.

Problem20: A laptop was sold for $770 after a 10% markup on its original price. What was the original price?

Solution:

1. Let the original price be x
   • After a 10% markup, the selling price is $770
   • 770=1.10x
2. Solve for x
   • Divide both sides by 1.10
   • x=770/1.10=700

Answer: The original price of the laptop was $700.

Problem21: A company has 200 employees. If 40% of the employees are women, how many women are there in the company?

Solution:

Convert the percentage to a decimal

40%=40/100=0.40

Multiply the decimal by the total number of employees

Number of women=0.40×200

=80

Answer: There are 80 women in the company.

Problem22: David received $75, which is 25% of his monthly salary. What is his total monthly salary?

Solution:

1. Let the total monthly salary be x
   • 25% of x is $75
   • 0.25x = 75
2. Solve for x
   • Divide both sides by 0.25
   • x=75/0.25​=300

Answer: David’s total monthly salary is $300.

Problem23: The price of a concert ticket increased from $50 to $65. What is the percentage increase?

Solution:

Find the increase in price: Increase=65−50=15

Calculate the percentage increase

Percentage increase=15/50×100=30%

Answer: The price increased by 30%.

Problem24: A laptop’s price dropped from $1,200 to $960. What is the percentage decrease?

Solution:

Find the decrease in price

Decrease=1,200−960=240

Calculate the percentage decrease

Percentage decrease=(240/1,200)×100

=20%

Answer: The price decreased by 20%.

Problem25: After a 30% discount, a pair of shoes costs $70. What was the original price?

Solution:

1. Let the original price be x
   • After a 30% discount, the shoes cost $70
   • 70=x−0.30x
   • 0.70x = 70
2. Solve for x
   • Divide both sides by 0.70
   • x=70/0.70=100

Answer: The original price of the shoes was $100.

Problem26: Out of 500 people in a survey, 125 prefer chocolate ice cream. What percentage of the people prefer chocolate ice cream?

Solution:

Calculate the percentage

Percentage of people who prefer chocolate ice crea

m

=(125/500)×100

=25%

Answer: 25% of the people prefer chocolate ice cream.

Problem27: A TV was sold for $660 after a 10% markup on its original price. What was the original price?

Solution:

1. Let the original price be x
   • After a 10% markup, the selling price is $660
   • 660=1.10x
2. Solve for x
   • Divide both sides by 1.10
   • x=660/1.10=600

Answer: The original price of the TV was $600.

Problem28: A class has 50 students. If 20% of the students received an A grade, how many students received an A grade?

Solution:

Convert the percentage to a decimal

20%=20/100=0.20

Multiply the decimal by the total number of students

Number of students with an A grade=0.20×50

=10

Answer: 10 students received an A grade.

Problem29: Emma saved $45, which is 15% of her total savings. What are her total savings?

Solution:

1. Let the total savings be x
   • 15% of x is $45
   • 0.15x=45
2. Solve for x
   • Divide both sides by 0.15:
   • x=45/0.15=300

Answer: Emma’s total savings are $300.

Problem30: The value of a car increased from $15,000 to $18,000. What is the percentage increase?

Solution:

Find the increase in value:

Increase=18,000−15,000=3,000

Calculate the percentage increase:

Percentage increase=(3,000/15,000)×100

=20%

Answer: The value of the car increased by 20%.

Problem31: A television’s price dropped from $500 to $400. What is the percentage decrease?

Solution:

Find the decrease in price

Decrease=500−400=100

Calculate the percentage decrease:

Percentage decrease=(100/500)×100=

20%

Answer: The price decreased by 20%.

Problem32: After a 25% discount, a bicycle costs $150. What was the original price?

Solution:

1. Let the original price be x
   • After a 25% discount, the bicycle costs $150
   • 150=x−0.25x
   • 150=0.75x
   • 150 = 0.75×150=0.75x
2. Solve for x
   • Divide both sides by 0.75
   • x=150/0.75=200

Answer: The original price of the bicycle was $200.

Problem33: Out of 800 employees in a company, 200 are in the sales department. What percentage of the employees are in the sales department?

Solution:

Calculate the percentage

Percentage of employees in the sales department=

(200/800)×100=25%

Answer: 25% of the employees are in the sales department.

Problem34: A smartphone was sold for $660 after a 10% markup on its original price. What was the original price?

Solution:

Let the original price be x

After a 10% markup, the selling price is $660

= 1.10x =660

Solve for x

Divide both sides by 1.10

x=660/1.10​=600

Answer: The original price of the smartphone was $600.

Problem35: Maria scored 85% on her final exam. If the exam had a total of 200 points, how many points did Maria score?

Solution: To find out how many points Maria scored, you need to calculate 85% of 200.

Step-by-step:

Convert the percentage to a decimal

85%=85/100=0.85

Multiply the total points by the decimal:

Points scored=200×0.85

Perform the multiplication

Points scored=170

Answer: So, Maria scored 170 points on her final exam.

Problem36: A jacket is on sale for 25% off. If the discount amount is $40, what was the original price of the jacket?

Solution: To find the original price, you need to determine what amount $40 represents 25% of.

Step-by-step:

Set up the equation where x is the original price

0.25x=40

Solve for x=40/0.25

Perform the division: x=160

Answer: So, the original price of the jacket was $160.

Problem37: The price of a laptop increased from $500 to $600. What is the percentage increase in the price?

Solution: To find the percentage increase, you need to calculate the difference in price, then divide by the original price and multiply by 100.

Step-by-step:

Calculate the difference in price

Difference=600−500=100

Divide the difference by the original price

100/500=0.2

Convert the decimal to a percentage

0.2×100=20%

Answer: So, the price of the laptop increased by 20%.

Problem38: A TV originally priced at $800 is now on sale for $600. What is the percentage decrease in the price?

Solution: To find the percentage decrease, you need to calculate the difference in price, then divide by the original price and multiply by 100.

Step-by-step:

Calculate the difference in price

Difference=800−600=200

Divide the difference by the original price

200/800=0.25

Convert the decimal to a percentage

0.25×100=25%

Answer: So, the price of the TV decreased by 25%.

Problem39: Out of 120 students in a class, 90 passed the exam. What percentage of students passed the exam?

The original price of the smartphone was $600.

Solution: To find the percentage of students who passed, you need to divide the number of students who passed by the total number of students, then multiply by 100.

Step-by-step:

Divide the number of students who passed by the total number of students:

90/120=0.75

Convert the decimal to a percentage

0.75×100=75%

Answer: So, 75% of the students passed the exam.

Problem40: Jenny bought a dress for $150 and received a discount of 20%. How much was the discount, and what was the final price of the dress?

Solution:

Calculate the discount amount:

Discount amount=Original price×(Discount percentage/100){100}

Discount amount=150×(20/100)=150×0.20=30

Calculate the final price after the discount:

Final price=Original price−Discount amount

150 – 30 = 120

Final price=150−30=120

Answer: So, the discount amount was $30, and the final price of the dress was $120.

Problem41: A car is sold for $18,000 after a 10% discount. What was the original price of the car?

Solution:

Let x be the original price.

Calculate the price after discount

Price after discount=x×(1−10/100)

=x×0.90

Set up the equation

x×0.90=18000

Solve for x

x=18000/0.90=20000

Answer: So, the original price of the car was $20,000.

Problem42: The price of a book increased from $25 to $30. What is the percentage increase?

Solution:

Calculate the difference in price:

Difference=30−25=5

Divide the difference by the original price:

Fraction increase=5/25=0.20

Convert the fraction to a percentage:

Percentage increase=0.20×100

=20%

Answer: So, the price of the book increased by 20%.

Problem43: The population of a town decreased from 50,000 to 45,000. What is the percentage decrease?

Solution:

Calculate the difference in population

Difference=50000−45000=5000

Divide the difference by the original population:

Fraction decrease=5000/50000

=0.10

Convert the fraction to a percentage

Percentage decrease=0.10×100=10%

Answer: So, the population of the town decreased by 10%.

Problem44: In a class of 40 students, 30 students passed the exam. What percentage of students passed the exam?

Solution:

Divide the number of students who passed by the total number of students:

Fraction passed=30/40=0.75

Convert the fraction to a percentage:

Percentage passed=0.75×100=75%

Answer: So, 75% of the students passed the exam.