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Mathematics LibreTexts

7.3: Solving Basic Percent Problems

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  • Page ID 22503

  • David Arnold
  • College of the Redwoods

There are three basic types of percent problems:

  • Find a given percent of a given number. For example, find 25% of 640.
  • Find a percent given two numbers. For example, 15 is what percent of 50?
  • Find a number that is a given percent of another number. For example, 10% of what number is 12?

Let’s begin with the first of these types.

Find a Given Percent of a Given Number

Let’s begin with our first example.

What number is 25% of 640?

Let x represent the unknown number. Translate the words into an equation.

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{25%} & \text{ of } & \colorbox{cyan}{640} \\ x & = & 25 \% & \cdot & 640 \end{array}\nonumber \]

Now, solve the equation for x.

\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 0.25 \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a decimal: 25% = 0.25.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Multiply: 0.25 \cdot 640 = 160.}} \end{aligned}\nonumber \]

Thus, 25% of 640 is 160.

Alternate Solution

We could also change 25% to a fraction.

\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{4} \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a fraction: 25% = 25/100 = 1/4.}} \\ x = \frac{640}{4} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Divide: 640/4 = 160.}} \end{aligned}\nonumber \]

Same answer.

What number is 36% of 120?

What is number \(8 \frac{1}{3} \%\) of 120?

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{8 (1/3)%} & \text{ of } & \colorbox{cyan}{120} \\ x & = & 8 \frac{1}{3} \% & \cdot & 120 \end{array}\nonumber \]

Now, solve the equation for x . Because

\[8 \frac{1}{3} \%= 8.3 \% = 0.08 \overline{3},\nonumber \]

working with decimals requires that we work with a repeating decimal. To do so, we would have to truncate the decimal representation of the percent at some place and satisfy ourselves with an approximate answer. Instead, let’s change the percent to a fraction and seek an exact answer.

\[ \begin{aligned} 8 \frac{1}{3} \% = \frac{8 \frac{1}{3}}{100} ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{25}{3}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper fraction.}} \\ = \frac{25}{3} \cdot \frac{1}{100} ~& \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{25}{300} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ = \frac{1}{12} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 25.}} \end{aligned}\nonumber \]

Now we can solve our equation for x .

\[ \begin{aligned} = 8 \frac{1}{3} \% \cdot 120 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{12} \cdot 120 ~ & \textcolor{red}{8 \frac{1}{3} \% = 1/12.} \\ x = \frac{120}{12} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 10 ~ & \textcolor{red}{ \text{ Divide: 120/12 = 10.}} \end{aligned}\nonumber \]

Thus, \(8 \frac{1}{3} \%\) of 120 is 10.

What number is \(4 \frac{1}{6} \%\) of 1,200?

What number is \(105 \frac{1}{4} \%\) of 18.2?

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{105 (1/4) %} & \text{ of } & 18.2 \\ x & = & 105 \frac{1}{4} \% & \cdot & 18.2 \end{array}\nonumber \]

In this case, the fraction terminates as 1/4=0.25, so

\[105 \frac{1}{4} \% = 105.25% = 1.0525.\nonumber \]

\[ \begin{aligned} x = 105 \frac{1}{4} \% \cdot 18.2 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 1.0525 \cdot 18.2 ~ & \textcolor{red}{5 \frac{1}{4} \% = 1.0525.} \\ x = 19.1555 ~ & \textcolor{red}{ \text{ Multiply.}} \end{aligned}\nonumber \]

Thus, \(105 \frac{1}{4} \%\) of 18.2 is 19.1555.

What number is \(105 \frac{3}{4} \%\) of 222?

Find a Percent Given Two Numbers

Now we’ll address our second item on the list at the beginning of the section.

15 is what percent of 50?

Let x represent the unknown percent. Translate the words into an equation.

\[ \begin{array}{c c c c} \colorbox{cyan}{15} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{50} \\ 15 & = & x & \cdot & 50 \end{array}\nonumber \]

The commutative property of multiplication allows us to change the order of multiplication on the right-hand side of this equation.

\[15 = 50x.\nonumber \]

\[ \begin{aligned} 15 = 50x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{15}{50} = \frac{50x}{50} ~ & \textcolor{red}{ \text{ Divide both sides by 50.}} \\ \frac{15}{50} = x ~ & \textcolor{red}{ \text{ Simplify right-hand side.}} \\ x = 0.30 ~ & \textcolor{red}{ \text{ Divide: 15/50 = 0.30.}} \end{aligned}\nonumber \]

But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol.

Screen Shot 2019-09-23 at 2.55.59 PM.png

Thus, 15 is 30% of 50.

Alternative Conversion

At the third step of the equation solution, we had

\[x = \frac{15}{50}.\nonumber \]

We can convert this to an equivalent fraction with a denominator of 100.

\[x = \frac{15 \cdot 2}{50 \cdot 2} = \frac{30}{100}\nonumber \]

Thus, 15/50 = 30/100 = 30%.

14 is what percent of 25?

10 is what percent of 80?

\[ \begin{array}{c c c c c} \colorbox{cyan}{10} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{80} \\ 10 & = & x & \cdot & 80 \end{array}\nonumber \]

The commutative property of multiplication allows us to write the right-hand side as

\[10 = 80x.\nonumber \]

\[ \begin{aligned} 10 = 80x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{10}{80} = \frac{80x}{80} ~ & \textcolor{red}{ \text{ Divide both sides by 80.}} \\ \frac{1}{8} = x ~ & \textcolor{red}{ \text{ Reduce: } 10/80 = 1/8.} \\ 0.125 = x ~ & \textcolor{red}{ \text{ Divide: } 1/8 = 0.125.} \end{aligned}\nonumber \]

Screen Shot 2019-09-23 at 3.00.38 PM.png

Thus, 10 is 12.5% of 80.

\[x = \frac{1}{8} .\nonumber \]

We can convert this to an equivalent fraction with a denominator of 100 by setting up the proportion

\[\frac{1}{8} = \frac{n}{100}\nonumber \]

Cross multiply and solve for n .

\[ \begin{aligned} 8n = 100 ~ & \textcolor{red}{ \text{ Cross multiply.}} \\ \frac{8n}{8} = \frac{100}{8} ~ & \textcolor{red}{ \text{ Divide both sides by 8.}} \\ n = \frac{25}{8} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 4.}} \\ n = 12 \frac{1}{2} ~ & \textcolor{red}{ \text{ Change 25/2 to mixed fraction.}} \end{aligned}\nonumber \]

\[ \frac{1}{8} = \frac{12 \frac{1}{2}}{100} = 12 \frac{1}{2} \%.\nonumber \]

10 is what percent of 200?

Find a Number that is a Given Percent of Another Number

Let’s address the third item on the list at the beginning of the section.

10% of what number is 12?

\[ \begin{array}{c c c c c} \colorbox{cyan}{10%} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } & \colorbox{cyan}{12} \\ 10 \% & \cdot & x & = & 12 \end{array}\nonumber \]

Change 10% to a fraction: 10% = 10/100 = 1/10.

\[ \frac{1}{10} x = 12\nonumber \]

\[ \begin{aligned} 10 \left( \frac{1}{10} x \right) = 10(12) ~ & \textcolor{red}{ \text{ Multiply both sides by 10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Thus, 10% of 120 is 12.

Alternative Solution

We can also change 10% to a decimal: 10% = 0.10. Then our equation becomes

\[0.10x = 12\nonumber \]

Now we can divide both sides of the equation by 0.10.

\[ \begin{aligned} \frac{0.10x}{0.10} = \frac{12}{0.10} ~ & \textcolor{red}{ \text{ Divide both sides by 0.10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Divide: 12/0.10 = 120.}} \end{aligned}\nonumber \]

20% of what number is 45?

\(11 \frac{1}{9} \%\) of what number is 20?

\[ \begin{array}{c c c c c} \colorbox{cyan}{11 (1/9) %} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } \colorbox{cyan}{20} \\ 11 \frac{1}{9} \% & \cdot & x & = & 20 \end{array}\nonumber \]

Change \(11 \frac{1}{9} \%\) to a fraction.

\[ \begin{aligned} 11 \frac{1}{9} \% ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{100}{9}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper: } 11 \frac{1}{9} = 100/9.} \\ = \frac{100}{9} \cdot \frac{1}{100} ~ & \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{ \cancel{100}}{9} \cdot \frac{1}{ \cancel{100}} ~ & \textcolor{red}{ \text{ Cancel.}} \\ = \frac{1}{9} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Replace \(11 \frac{1}{9} \%\) with 1/9 in the equation and solve for x .

\[ \begin{aligned} \frac{1}{9} x = 20 ~ & ~ \textcolor{red}{11 \frac{1}{9} \% = 1/9/} \\ 9 \left( \frac{1}{9} x \right) = 9(20) ~ & \textcolor{red}{ \text{ Multiply both sides by 9.}} \\ x = 180 \end{aligned}\nonumber \]

Thus, \(11 \frac{1}{9} \%\) of 180 is 20.

\(12 \frac{2}{3} \%\) of what number is 760?

1. What number is 22.4% of 125?

2. What number is 159.2% of 125?

3. 60% of what number is 90?

4. 25% of what number is 40?

5. 200% of what number is 132?

6. 200% of what number is 208?

7. 162.5% of what number is 195?

8. 187.5% of what number is 90?

9. 126.4% of what number is 158?

10. 132.5% of what number is 159?

11. 27 is what percent of 45?

12. 9 is what percent of 50?

13. 37.5% of what number is 57?

14. 162.5% of what number is 286?

15. What number is 85% of 100?

16. What number is 10% of 70?

17. What number is 200% of 15?

18. What number is 50% of 84?

19. 50% of what number is 58?

20. 132% of what number is 198?

21. 5.6 is what percent of 40?

22. 7.7 is what percent of 35?

23. What number is 18.4% of 125?

24. What number is 11.2% of 125?

25. 30.8 is what percent of 40?

26. 6.3 is what percent of 15?

27. 7.2 is what percent of 16?

28. 55.8 is what percent of 60?

29. What number is 89.6% of 125?

30. What number is 86.4% of 125?

31. 60 is what percent of 80?

32. 16 is what percent of 8?

33. What number is 200% of 11?

34. What number is 150% of 66?

35. 27 is what percent of 18?

36. 9 is what percent of 15?

37. \(133 \frac{1}{3} \%\) of what number is 80?

38. \(121 \frac{2}{3} \%\) of what number is 73?

39. What number is \(54 \frac{1}{3} \%\) of 6?

40. What number is \(82 \frac{2}{5} \%\) of 5?

41. What number is \(62 \frac{1}{2} \%\) of 32?

42. What number is \(118 \frac{3}{4} \%\) of 32?

43. \(77 \frac{1}{7} \%\) of what number is 27?

44. \(82 \frac{2}{3} \%\) of what number is 62?

45. What number is \(142 \frac{6}{7} \%\) of 77?

46. What number is \(116 \frac{2}{3} \%\) of 84?

47. \(143 \frac{1}{2} \%\) of what number is 5.74?

48. \(77 \frac{1}{2} \%\) of what number is 6.2?

49. \(141 \frac{2}{3} \%\) of what number is 68?

50. \(108 \frac{1}{3} \%\) of what number is 78?

51. What number is \(66 \frac{2}{3} \%\) of 96?

52. What number is \(79 \frac{1}{6} \%\) of 48?

53. \(59 \frac{1}{2} \%\) of what number is 2.38?

54. \(140 \frac{1}{5} \%\) of what number is 35.05?

55. \(78 \frac{1}{2} \%\) of what number is 7.85?

56. \(73 \frac{1}{2} \%\) of what number is 4.41?

57. What number is \(56 \frac{2}{3} \%\) of 51?

58. What number is \(64 \frac{1}{2} \%\) of 4?

59. What number is \(87 \frac{1}{2} \%\) of 70?

60. What number is \(146 \frac{1}{4} \%\) of 4?

61. It was reported that 80% of the retail price of milk was for packaging and distribution. The remaining 20% was paid to the dairy farmer. If a gallon of milk cost $3.80, how much of the retail price did the farmer receive?

62. At $1.689 per gallon of gas the cost is distributed as follows:

\[ \begin{aligned} \text{Crude oil supplies } & ~ $0.95 \\ \text{Oil Companies } & ~ $0.23 \\ \text{State and City taxes } & ~ $0.23 \\ \text{Federal tax } & ~ $0.19 \\ \text{Service Station } & ~ $0.10 \end{aligned}\nonumber \]

Data is from Money, March 2009 p. 22, based on U. S. averages in December 2008. Answer the following questions rounded to the nearest whole percent.

a) What % of the cost is paid for crude oil supplies?

b) What % of the cost is paid to the service station?

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Step by step guide to solve percent problems

  • In each percent problem, we are looking for the base, or part or the percent.
  • Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

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Download Percent Problems Worksheet

  • \(\color{blue}{15}\)
  • \(\color{blue}{104.3}\)
  • \(\color{blue}{38.34}\)
  • \(\color{blue}{23.44\%}\)
  • \(\color{blue}{47.6\%}\)
  • \(\color{blue}{100}\)

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Course: 6th grade   >   Unit 3

  • Finding a percent

Finding percents

  • Your answer should be
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Enter the value(s) for the required question and click the adjacent Go button.

PERCENTAGES

This section will explain how to apply algebra to percentage problems.

In algebra problems, percentages are usually written as decimals.

Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?

The number of questions correct is indicated by:

percentage problem solving maths genie

Ethan got 44 questions correct.

Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.

Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

percentage problem solving maths genie

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

percentage problem solving maths genie

Darrel’s grade for the course is an 89.6, or a B+.

b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?

The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.

So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

percentage problem solving maths genie

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.

Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.

a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).

Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

percentage problem solving maths genie

b. Simplify the equation.

percentage problem solving maths genie

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.

c. Solve the equation when the sale price is $97.

percentage problem solving maths genie

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)

The following diagram is meant as a visualization of problem 3.

percentage problem solving maths genie

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount

Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.

Study Tip: Remember to use descriptive letters to describe the variables.

CHAPTER 1 REVIEW

This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Informal Rules:

Adding or subtracting like signs: Add the two numbers and use the common sign.

percentage problem solving maths genie

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

percentage problem solving maths genie

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

percentage problem solving maths genie

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

percentage problem solving maths genie

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

percentage problem solving maths genie

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

percentage problem solving maths genie

Simplifying Algebraic Equations:

percentage problem solving maths genie

Combine like terms:

percentage problem solving maths genie

Solving Equations:

1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

percentage problem solving maths genie

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

percentage problem solving maths genie

c. If the call costs $23.50, how long were you on the phone?

percentage problem solving maths genie

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.

percentage problem solving maths genie

Percentages:

Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

percentage problem solving maths genie

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

percentage problem solving maths genie

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.

Math Topics

More solvers.

  • Add Fractions
  • Simplify Fractions

Solved Examples on Percentage

The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage.

Solved examples on percentage:

1.  In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.

Total number of invalid votes = 15 % of 560000

                                       = 15/100 × 560000

                                       = 8400000/100

                                       = 84000

Total number of valid votes 560000 – 84000 = 476000

Percentage of votes polled in favour of candidate A = 75 %

Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000

= 75/100 × 476000

= 35700000/100

2. A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.

Total number of fruits shopkeeper bought = 600 + 400 = 1000

Number of rotten oranges = 15% of 600

                                    = 15/100 × 600

                                    = 9000/100

                                    = 90

Number of rotten bananas = 8% of 400

                                   = 8/100 × 400

                                   = 3200/100

                                   = 32

Therefore, total number of rotten fruits = 90 + 32 = 122

Therefore Number of fruits in good condition = 1000 - 122 = 878

Therefore Percentage of fruits in good condition = (878/1000 × 100)%

                                                                 = (87800/1000)%

                                                                 = 87.8%

3. Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?

Solution:            

Let the money he took for shopping be m.

Money he spent = 30 % of m

                      = 30/100 × m

                      = 3/10 m

Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10

But money left with him = $ 2100

Therefore 7m/10 = $ 2100          

m = $ 2100× 10/7

m = $ 21000/7

Therefore, the money he took for shopping is $ 3000.

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

Ratio into Percentage

Percentage into Decimal

Decimal into Percentage

Percentage of the given Quantity

How much Percentage One Quantity is of Another?

Percentage of a Number

Increase Percentage

Decrease Percentage

Basic Problems on Percentage

Problems on Percentage

Real Life Problems on Percentage

Word Problems on Percentage

Application of Percentage

8th Grade Math Practice From Solved Examples on Percentage to HOME PAGE

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Percentage Worksheets Percentages of Numbers

Welcome to our Finding Percentage Worksheets. In this area, we have a selection of percentage worksheets for 6th graders designed to help children learn and practice finding percentages of numbers.

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  • How to Find Percentages of a Number
  • Finding Simple Percentages Worksheets
  • Finding Simple Percentages Online Quiz
  • Finding Harder Percentages Worksheets
  • Finding (Harder) Percentages Online Quiz
  • More related Math resources

Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

  • 50% = 0.5 = ½
  • 25% = 0.25 = ¼
  • 75% = 0.75 = ¾
  • 10% = 0.1 = 1 ⁄ 10
  • 1% = 0.01 = 1 ⁄ 100

Percentage Worksheets

How to work out percentages of a number.

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

  • How to find percentage of numbers support

Finding Percentage Worksheets

Here you will find a selection of worksheets on percentages designed to help your child understand how to work out percentages of different numbers.

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

  • finding simple percentages 1%, 10%, 50% and 100%;
  • finding multiples of 5%;
  • finding any percentage of a number.

The percentage worksheets have been designed for students in 6th grade, and all the sheets come with an answer sheet.

Finding Simple Percentages (1%, 10%, 50% and 100%)

These sheets are a great way to start off learning percentages.

All the questions involve finding either 1%, 10%, 50% or 100% of different numbers.

  • Finding Simple Percentages 1
  • PDF version
  • Finding Simple Percentages 2
  • Finding Simple Percentages 3

Finding Simple Percentages Quiz

Our quizzes have been created using Google Forms.

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This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your understanding and skill at finding simple percentages of different amounts.

Fun Quiz Facts

  • This quiz was attempted 1,329 times last academic year. The average (mean) score was 13.4 out of 19 marks.
  • Can you beat the mean score?

Finding Harder Percentages

  • Find Percentages 1
  • Find Percentages 2
  • Find Percentages 3
  • Find Percentages 4
  • Find Percentages 5

Finding Percentages Walkthrough Video

This short video walkthrough shows several problems from our Finding Percentages Worksheet 3 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Finding Percentages Quiz

This quick quiz tests your understanding and skill at finding a range of percentages of different amounts.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

  • Money Percentage Worksheets

Percentage Word Problems

Once your child is confident finding percentages of a range of numbers, they can start using their knowledge to solve problems involving percentages.

The worksheets in this section contain a range of percentage problems set in different contexts.

  • Percentage Word Problems 5th Grade
  • 6th Grade Percent Word Problems

How can I work out the percentage increase (or decrease)?

Take a look at our How to Work Out Percentage Increase/Decrease page.

This page is all about finding the percentage increase or decrease between two numbers.

We also have a percentage increase calculator that will work it all out for you at the click of a button.

  • How to Work out the Percentage Increase or Decrease

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

Convert fractions to percentages Picture

  • Converting Fractions to Percentages

Convert Percent to Fraction Image

  • Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

  • Online Percentage Practice

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Maths Genie GCSE Questions & Answers

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GCSE Maths

Percentage Profit

Here we will learn about percentage profit, including what percentage profit is and how to solve problems involving percentage profit.

There are also percentage profit worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is percentage profit?

Percentage profit is writing a profit as a percentage. This makes it easier to compare with other profits.

To do this you need to find the profit and change this into a percentage of the original amount (the cost of the item at the start). Calculating profit is done by finding the difference between the cost price and the selling price.

You can use this formula to calculate the profit percentage,

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100 .

For example, I bought a painting for £200. I sold it for £230. So the profit I have made is £30 as this is the difference between the cost price and the selling price.

The percentage profit is 15\%.

The amount of money the item is bought for at the start can be called the cost price (or cost of goods sold).

The amount of money the item is sold for later in the question can be called the sale price or the selling price .

This can be extended into calculating percentage loss. This is when the value has gone down over time (known as depreciation).

This skill is very useful for business owners.

What is percentage profit?

How to calculate percentage profit

In order to calculate percentage profit:

Calculate the difference between the cost price and the selling price.

Express the profit (or loss) as a fraction of the original amount and multiply by \bf{100} .

Write down the final answer.

Explain how to calculate percentage profit

Explain how to calculate percentage profit

Percentage profit worksheet

Get your free percentage profit worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Percentage profit examples

Example 1: calculating percentage profit.

Ron bought an antique train set for £130.

He sold it for £215.

Calculate the percentage profit Ron made.

Give your answer to the nearest percent.

  • Calculate the difference between the cost price and the selling price. 

The difference is,

2 Express the profit (or loss) as a fraction of the original amount and multiply by \bf{100} .

You can find the percentage profit by making a fraction and multiplying by 100.

3 Write down the final answer.

The percentage profit Ron made is \bf{65\%} to the nearest percent.

Example 2: calculating percentage profit

Ellen buys a house for £210 \ 000. She sells the house for £226 \ 500.

Calculate the percentage profit Ellen makes. Give your answer to 1 decimal place.

226 \ 500-210 \ 000=16 \ 500.

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{16 \ 500}{210 \ 000}\times 100=7.857…

The percentage profit Ellen makes is \bf{7.9\%} to 1 decimal place.

Example 3: calculating percentage loss

Diane bought an antique vase for £95.

She sold it for £78.

Calculate the percentage loss Diane made.

Give your answer to 3 significant figures.

You can find the percentage loss by making a fraction and multiplying by 100.

\text{Percentage loss}=\cfrac{\text{loss}}{\text{original}}\times 100=\cfrac{17}{95}\times 100=17.894…

The percentage loss Diane made is \bf{17.9\%} to 3 significant figures.

Example 4: calculating percentage loss

Rahul bought a van for £16 \ 500.

He sold it for £9 \ 350.

Calculate the percentage loss Rahul made.

16 \ 500-9 \ 350=7 \ 150.

\text{Percentage loss}=\cfrac{\text{loss}}{\text{original}}\times 100=\cfrac{7 \ 150}{16 \ 500}\times 100=43.333…

The percentage loss Rahul makes is \bf{43.3\%} to 3 significant figures.

Example 5: problem solving

Katie buys a pack of 12 bottles of water for £3.50.

She sells the water at 80p per bottle.

Work out Katie’s percentage profit.

First you need to calculate the total selling price (or total sales).

12\times 80=960

The total selling price is £9.60

£9.60-£3.50=£6.10 .

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{6.10}{3.50}\times 100=174.285…

The percentage profit Katie makes is \bf{174\%}.

Example 6: problem solving

Ranjeev buys 20 jackets at £25 each.

He sells 15\% of them for £50 each and half of them for £35. He sells the rest for £12 each.

Work out Ranjeev’s percentage profit or loss.

State clearly if Ranjeev makes a profit or a loss.

First you need to calculate the total cost price (or cost of goods sold).

20\times \pounds25=\pounds500

Then you need to work out the total selling price (or total sales).

15\% of 20 is 3 jackets, so he sells 3 jackets at £50. He also sells 10 jackets at £35 and 7 jackets at £12.

The total selling price is,

(3\times \pounds50) + (10\times \pounds35) + (7\times \pounds12)=\pounds584.

Ranjeev sells the jackets for more than he bought them for, so he has made a profit.

584-500=84 .

\text{Percentage profit}=\cfrac{\text{profit}}{\text{original}}\times 100=\cfrac{84}{500}\times 100=16.8

Ranjeev makes a profit and the percentage profit is \bf{16.8\%}.

Common misconceptions

  • Always use the original cost price as the denominator

The original cost price is always used as the denominator in the percentage formula for profit.

  • Be consistent with pounds and pence

Sometimes questions may give one amount of money in pence (p), and another amount of money in pounds (£). When you calculate the percentage profit (or loss) make sure you use the same type of monetary units in your fraction. Whichever you use will give the same percentage profit.

  • Percentage profits can be more than \bf{100}

When calculating percentages for profits, they can be greater than 100\%. For example, if I buy a bottle of water for £0.50 and I sell it for £2, I made £1.50 profit which is 300\% profit. I sold the bottle for 4 times more than I originally bought it for.

Related lessons

Reverse percentages is part of our series of lessons to support revision on percentages. You may find it helpful to start with the main percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

  • Percentages
  • Percentage increase
  • Percentage decrease
  • Percentage of an amount
  • Percentage multipliers
  • Percentage change
  • One number as a percentage of another
  • Reverse percentages

Practice percentage profit questions

1. A trailer is bought for £50 and is sold for £60. Find the percentage profit.

GCSE Quiz True

The profit is £10.

The percentage profit is 20\%.

2. A flat is bought for £120 \ 000 and is sold for £145 \ 000. Find the percentage profit. Give your answer to the nearest percent.

The profit is £25 \ 000.

The percentage profit is 21\% (to the nearest percent).

3. A motorbike is bought for £995 and is sold for £850. Find the percentage loss. Give your answer to the nearest percent.

The loss is £145.

The percentage loss is 15\% (to the nearest percent).

4. A flat is bought for £120 \ 000 and is sold for £106 \ 500. Find the percentage loss. Give your answer to the nearest percent.

The loss is £13500.

The percentage loss is 11\% (to the nearest percent).

5. Molly buys 24 packets of crisps for £8.95. She sells the packets of crisps for 50p each. Calculate the percentage profit. Give your answer to 3 significant figures.

The selling price of the crisps is,

The profit is £3.05.

The percentage profit is 34.1\% (to 3 significant figures).

6. Yago buys 200 books for £4 each. He sells \cfrac{3}{4} of the books for £6.50 each and the rest for £1 each. Calculate the percentage profit or loss, stating clearly if there is a profit or a loss. Give your answer to one decimal place.

Loss 28.1\%

Profit 28.1\%

Loss 21.8\%

Profit 21.8\%

The cost of the books is,

200\times \pounds4=\pounds800 .

The selling price of the books is,

(150\times \pounds6.50)+(50\times \pounds1)=\pounds1025 .

The profit is £225.

The percentage profit is 28.1\% (to the nearest percent).

Percentage profit GCSE questions

1. A small business buys phones for £45 each and sells them for £75.

Calculate the percentage profit for each phone. Give your answer to 1 decimal place.

2. (a) Malcolm buys a bike for £800.

He sells it to Gordon for £500.

Calculate Malcolm’s percentage loss.

(b) Gordon then sells the bike to Samir for £540.

Calculate Gordon’s percentage profit.

3. Sundeep is a business owner of a small business.

He buys 40 games consoles at £65 each.

He sells a quarter of the games consoles for £100 each.

He sells 35\% of the games consoles for £75 each.

He sells the rest for £30 each.

Calculate the percentage profit or loss for Sundeep.

State clearly if it is a percentage profit or loss.

Give your answer correct to 3 significant figures.

LOSS of 2.69\%

Learning checklist

You have now learned how to:

  • Calculate percentage profit
  • Calculate percentage loss
  • Solve problems involving percentage profit

The next lessons are

  • Comparing fractions, decimals and percentages
  • Powers and roots

Still stuck?

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COMMENTS

  1. Maths Genie • Percentages

    27% = 0.27. We type 0.27 × 350 into the calculator: This gives an answer of 189 2, we can press the SD button to get a decimal answer: 189 2 = 94.5. A percentage is the same as a fraction out of 100, we can We can convert percentages to fractions. by writing them over 100. 55% = 55 100. 9% = 9 100. 87% = 87 100. 29% = 29 100.

  2. Maths Genie

    Upcoming A Level Exams. Paper 1: Tuesday 04 June 2024 (PM) Paper 2: Tuesday 11 June 2024 (PM) Paper 3: Thursday 20 June 2024 (PM) If you find any mistakes, or if you have any feedback, please email: [email protected]. Maths Genie is a free GCSE and A Level revision site. It has past papers, mark schemes and model answers to GCSE and A ...

  3. 5.2.1: Solving Percent Problems

    Solution. 20 100 = amount base. The percent in this problem is 20%. Write this percent in fractional form, with 100 as the denominator. 20 100 = 30 n. The percent is written as the ratio 20 100, the amount is 30, and the base is unknown. 20 ⋅ n = 30 ⋅ 100 20 ⋅ n = 3, 000 n = 3, 000 ÷ 20 n = 150.

  4. 7.3: Solving Basic Percent Problems

    Now we can solve our equation for x. 15 = 50 x Original equation. 15 50 = 50 x 50 Divide both sides by 50. 15 50 = x Simplify right-hand side. x = 0.30 Divide: 15/50 = 0.30. But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol.

  5. Percentages Practice Questions

    The Corbettmaths Practice Questions on finding a percentage of an amount.

  6. Percentages

    Math; Pre-algebra; Unit 4: Percentages. 700 possible mastery points. Mastered. Proficient. Familiar. Attempted. Not started. Quiz. Unit test. ... Percent word problems Get 5 of 7 questions to level up! Quiz 3. Level up on the above skills and collect up to 160 Mastery points Start quiz. Up next for you:

  7. How to Solve Percent Problems? (+FREE Worksheet!)

    Percent Problems Percent Problems - Example 1: \(2.5\) is what percent of \(20\)? Solution: In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\) The Absolute Best Books to Ace Pre-Algebra to Algebra II

  8. Ratios, Fractions and Percentage Problems! Common Exam ...

    Join this channel to get access to perks:https://www.youtube.com/channel/UCStPzCGyt5tlwdpDXffobxA/joinA video revising the techniques and strategies for solv...

  9. Percentages

    p = a b × 100. This equation can be rearranged to show a or b in terms of the other values: a = p 100 × b b = a ( p 100) = 100 × a p. [Examples] In word problems involving percentages, remember that the sum of all parts of the whole is 100 % . For example, if a teacher has graded 60 % of an assignment, then they have not graded 100 − 60 % ...

  10. Finding percents (practice)

    Finding percents. 1 is 25 % of what number? Stuck? Review related articles/videos or use a hint. Report a problem. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone ...

  11. Percentage Calculator

    There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula. Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage: ... Do the math: 0.10 * 150 = 15; Y = 15; So 10% of 150 is 15;

  12. Percent Maths Problems

    Problem 6. A number increases from 30 to 40 and then decreases from 40 to 30. Compare the percent of increase from 30 to 40 and that of the decrease from 40 to 30. Solution to Problem 6. Percent increase from 30 to 40 is given by. (40 - 30) / 30 = 10 / 30 = 0.33 = 33% (2 significant digits) Percent decrease from 40 to 30 is given by.

  13. Calculate percentages with Step-by-Step Math Problem Solver

    Explanation: % means "per one hundred". So 80% means 80/100 = 0.80. Example 2. A math teacher, Dr. Pi, computes a student's grade for the course as follows: a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam. Wrote percents as decimals.

  14. PDF Name: GCSE (1

    Ratio Problems 2 Name: _____ Instructions • Use black ink or ball-point pen. • Answer all questions. • Answer the questions in the spaces provided - there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information

  15. Different Types of Percentage Problems

    The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage. Solved examples on percentage: 1. In an election, candidate A got 75% of the total valid votes.

  16. Finding Percentage Worksheets

    Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals. Key percentage facts: 50% = 0.5 = ½. 25% = 0.25 = ¼. 75% = 0.75 = ¾.

  17. Maths Genie Past Papers Questions & Answers

    These are free GCSE Maths Genie resources that we have pulled together from Maths Genie to help you revise your GCSE Maths. ... Equations 28 Ratio Factor Problems 29 Rearranging Harder Formula 30 Recurring Decimals To Fractions 31 Repeated Percentage Change 32 ... 24 Quadratic Formula 25 Quadratic Inequalities 26 Quadratic Sequences 27 ...

  18. Percentage Profit

    The difference is, 226 \ 500-210 \ 000=16 \ 500. 226 500 − 210 000 = 16 500. Express the profit (or loss) as a fraction of the original amount and multiply by \bf {100} 100. Show step. You can find the percentage profit by making a fraction and multiplying by 100. 100.