There is a confusion Percentage Calculation Table on internet. Therefore, in this post we will cover all that important stuff regarding Percentage.
We have covered Different Percentage Tables, Chart and Tools. Also we have covered some solved example regarding it that we often get in exams.
We will cover it from the basics to advanced. Make sure you read and understand the each till the very end.
Percentage and Formula
In math, a percentage is just a fancy way of expressing a part of a whole, where the whole is represented by the number 100. The word “percent” literally means “per hundred.” It’s a way of comparing a part to the whole on a scale of 100.
When you want to find a percentage of a number, you follow these steps:
- Divide by the Whole:
- Take the part you’re interested in (let’s call it the “part”).
- Divide it by the whole or the total (let’s call it the “whole”).
- Multiply by 100:
- Multiply the result from step 1 by 100.
Formula:
$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$
How To Calculate Percentage Of Marks: Any Number Of Subjects
Percentage Calculation Table
Here are three types of percentage calculation table that help you find percentage values, increment and decrement of percentage and reverse percentage.
Finding a Percentage of a Value
| Original Value | Percentage | Result |
|---|---|---|
| 150 | 25% | 37.5 |
| 250 | 8% | 20 |
| 300 | 50% | 150 |
| 120 | 15% | 18 |
| 180 | 30% | 54 |
| Formula | $\(\text{Original} \times \frac{\text{Percentage}}{100}\)$ | |
In this table, you have an “Original Value” and a “Percentage.” The “Result” column shows the calculated value when you find a percentage of the original value using the provided formula.
Let’s take the first row as an example:
- Original Value: 150
- Percentage: 25%
Now, apply the formula:
$\text{Result} = \text{Original} \times \left(\frac{\text{Percentage}}{100}\right)$
For the first row:
$\text{Result} = 150 \times \left(\frac{25}{100}\right) = 150 \times 0.25 = 37.5$
So, the result for the first row is (37.5).
You can follow the same process for each row in the table to find the percentage of the original value and calculate the result.
The formula helps you determine what portion of the original value the specified percentage represents.
| Original Value | Percentage | Result |
|---|---|---|
Finding the Percentage Increase or Decrease
| Initial Value | Final Value | Percentage Change |
|---|---|---|
| 100 | 120 | 20% Increase |
| 200 | 150 | 25% Decrease |
| 80 | 100 | 25% Increase |
| 300 | 240 | 20% Decrease |
| 150 | 180 | 20% Increase |
| Formula | $\(\frac{{\text{Final} – \text{Initial}}}{{\text{Initial}}} \times 100\)$ | |
Certainly! Let’s discuss the concept of compound interest using a simple example.
Example:
Suppose you invest 1,000 in a savings account that offers an annual interest rate of 5%. The interest is compounded annually, meaning that interest is added to the principal at the end of each compounding period.
Formula:
The formula for compound interest is given by the following formula:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$
Where:
- ( A ) is the future value of the investment/loan, including interest.
- ( P ) is the principal amount (the initial amount of money).
- ( r ) is the annual interest rate (as a decimal).
- ( n ) is the number of times that interest is compounded per unit ( t ) (time).
- ( t ) is the time the money is invested/borrowed for, in years.
Now, let’s apply this formula to the example:
Given:
- Principal amount (( P )): 1,000
- Annual interest rate (( r )): 5% or 0.05 (as a decimal)
- Number of times compounded per year (( n )): 1 (compounded annually)
- Time (( t )): 3 years
Plug the values into the formula:
A = 1000 $\left(1 + \frac{0.05}{1}\right)^{1 \times 3}$
Calculate:
$A = 1000 \times (1.05)^3$
Again $A = 1000 \times 1.157625$
Now; $A \approx 1157.63$
So, after 3 years, the future value of the investment will be approximately $1157.63. The interest earned is $1157.63 – $1000 = $157.63.
Calculating Reverse Percentage
| Original Value | New Value | Percentage Change |
|---|---|---|
| 80 | 100 | 25% Increase |
| 150 | 120 | 20% Decrease |
| 200 | 250 | 25% Increase |
| 120 | 100 | 16.67% Decrease |
| 250 | 200 | 20% Decrease |
| Formula | $\(\left(\frac{{\text{New} – \text{Original}}}{{\text{Original}}}\right) \times 100\)$ | |
Suppose you have a product that was initially priced at Rs. 80, and it undergoes a 20% price increase. The goal is to find the original price before the increase.
Formula:
The formula for calculating the original value before a percentage change is:
$\text{Original Value} = \frac{\text{New Value}}{1 + \left(\frac{\text{Percentage Change}}{100}\right)}$
Given:
- New Value: Rs. 80 (after the 20% increase)
Plug the values into the formula:
Original Value=801+(20/100)Original Value=1+(20/100)80
Calculate:
$\text{Original Value} = \frac{80}{1 + \left(\frac{20}{100}\right)}$
$\text{Original Value} = \frac{80}{1.20} \approx 66.67$
So, the original price of the product before the 20% increase was approximately $66.67.
This formula is useful when you know the final value after a percentage change and want to find the original value.
It involves dividing the new value by a factor that accounts for the percentage change. In this example, dividing by 1.201.20 adjusts for the 20% increase.
Percentage Chart Table
| S.no | Ratio | Fraction | Percent(%) | Decimal |
| 1 | 1:1 | 1/1 | 100 | 1 |
| 2 | 1:2 | 1/2 | 50 | 0.5 |
| 3 | 1:3 | 1/3 | 33.333 | 0.3333 |
| 4 | 1:4 | 1/4 | 25 | 0.25 |
| 5 | 1:5 | 1/5 | 20 | 0.20 |
| 6 | 1:6 | 1/6 | 16.667 | 0.16667 |
| 7 | 1:7 | 1/7 | 14.285 | 0.14285 |
| 8 | 1:8 | 1/8 | 12.5 | 0.125 |
| 9 | 1:9 | 1/9 | 11.111 | 0.11111 |
| 10 | 1:10 | 1/10 | 10 | 0.10 |
| 11 | 1:11 | 1/11 | 9.0909 | 0.0909 |
| 12 | 1:12 | 1/12 | 8.333 | 0.08333 |
| 13 | 1:13 | 1/13 | 7.692 | 0.07692 |
| 14 | 1:14 | 1/14 | 7.142 | 0.07142 |
| 15 | 1:15 | 1/15 | 6.66 | 0.0666 |
10 Computing a Percentage From a Table of Values
Here 20 question based on Percentage Calculation Table Of Values with there step by step solution
Percentage Calculation Table Of Values Question 1:
Q: In a class of seventh graders, students were asked to choose between playing soccer and tennis as their favorite sport. The results are tabulated below. Find the percentage of students whose favorite sport is soccer?
| Soccer | Tennis | |
|---|---|---|
| Boys | 18 | 12 |
| Girls | 10 | 15 |
Step-by-Step Answer:
Calculate the total number of students who like soccer
=18 (boys) + 10 (girls) = 28 students
Calculate the total number of students:
=18+12+10+15+18+12+10+15
=110 students
Calculate the percentage of students who like soccer:
$(\frac{\text{Total soccer players}}{\text{Total students}} \times 100)$
$\frac{28}{110} \times 100 $
$\frac{28}{110} \times 100 \approx 25.4545\%$
So, $(\frac{28}{110} \times 100)$ is approximately $(25.45\%)$.
Percentage Calculation Table Of Values Question 2:
Q: In a survey of eighth graders, students were asked to choose their preferred activity, either painting or sculpting. The results are tabulated below. Determine the percentage of students who enjoy sculpting?
| Painting | Sculpting | |
|---|---|---|
| Boys | 15 | 10 |
| Girls | 8 | 12 |
Step-by-Step Answer:
Calculate the total number of students who like sculpting:
$10 \, (\text{boys}) + 12 \, (\text{girls}) = 22$
Calculate the total number of students:
$15 \, (\text{boys}) + 10 \, (\text{boys painting}) + 8 \, (\text{girls}) + 12 \, (\text{girls sculpting}) = 45$
Calculate the percentage of students who like sculpting:
$\frac{\text{Total students who like sculpting}}{\text{Total students}} \times 100 = \frac{22}{45} \times 100 \approx 48.89\%$
Therefore, the percentage of students who like sculpting is approximately $(48.89\%)$.
Percentage Calculation Table Of Values Question 3:
Q:Among sixth graders, students were asked to choose between science and art as their favorite subject. The results are tabulated below. Find the percentage of students whose favorite subject is science?
| Science | Art | |
|---|---|---|
| Boys | 12 | 8 |
| Girls | 15 | 10 |
Step-by-Step Answer:
Calculate the total number of students who like science:
$12 \, (\text{boys}) + 15 \, (\text{girls}) = 27$
Calculate the total number of students:
$12 \, (\text{boys}) + 8 \, (\text{boys art}) + 15 \, (\text{girls}) + 10 \, (\text{girls art}) = 45$
Calculate the percentage of students who like science:
$\frac{\text{Total students who like science}}{\text{Total students}} \times 100 = \frac{27}{45} \times 100 \approx 60\%$
Therefore, the percentage of students who like science is approximately $(60\%)$.
Percentage Calculation Table Of Values Question 4:
Q: In a class of fifth graders, students were asked to choose between music and dance as their favorite extracurricular activity. The results are tabulated below. Determine the percentage of students whose favorite activity is dance?
| Music | Dance | |
|---|---|---|
| Boys | 10 | 15 |
| Girls | 12 | 8 |
Step-by-Step Answer:
Calculate the total number of students who like dance:
$15 \, (\text{boys}) + 8 \, (\text{girls}) = 23$
Calculate the total number of students:
$10 \, (\text{boys}) + 15 \, (\text{boys dance}) + 12 \, (\text{girls}) + 8 \, (\text{girls dance}) = 45$
Calculate the percentage of students who like dance:
$\frac{\text{Total students who like dance}}{\text{Total students}} \times 100 = \frac{23}{45} \times 100 \approx 51.11\%$
Therefore, the percentage of students who like dance is approximately $(51.11\%)$
Percentage Calculation Table Of Values Question 5:
Q: Among ninth graders, students were surveyed on their preference for reading or watching movies. The results are tabulated below. Find the percentage of students who prefer reading?
| Reading | Movies | |
|---|---|---|
| Boys | 20 | 15 |
| Girls | 18 | 12 |
Step-by-Step Answer:
Calculate the total number of students who like reading:
$20 \, (\text{boys}) + 18 \, (\text{girls}) = 38$
Calculate the total number of students:
$20 \, (\text{boys}) + 15 \, (\text{boys movies}) + 18 \, (\text{girls}) + 12 \, (\text{girls movies}) = 65$
Calculate the percentage of students who like reading:
$\frac{\text{Total students who like reading}}{\text{Total students}} \times 100 = \frac{38}{65} \times 100 \approx 58.46\%$
Therefore, the percentage of students who like reading is approximately $(58.46\%)$.
Percentage Calculation Table Of Values Question 6:
Q: In a survey conducted at a company picnic, employees were asked to choose between playing volleyball and badminton. The results are tabulated below. Find the percentage of employees whose favorite sport is volleyball?
| Volleyball | Badminton | |
|---|---|---|
| Executives | 10 | 5 |
| Administrative Staff | 8 | 12 |
Step-by-Step Answer:
- Calculate the total number of employees who like volleyball:
$10 \, (\text{executives}) + 8 \, (\text{administrative staff}) = 18$ - Calculate the total number of employees:
$10 \, (\text{executives}) + 5 \, (\text{executives badminton}) + 8 \, (\text{administrative staff}) + 12 \, (\text{administrative staff badminton}) = 35$ - Calculate the percentage of employees who like volleyball:
$\frac{\text{Total employees who like volleyball}}{\text{Total employees}} \times 100 = \frac{18}{35} \times 100 \approx 51.43\%$
Therefore, the percentage of employees who like volleyball is approximately $(51.43\%)$.
Percentage Calculation Table Of Values Question 7:
Q: In a neighborhood survey, residents were asked to choose between gardening and hiking as their preferred outdoor activity. The results are tabulated below. Determine the percentage of residents whose favorite activity is hiking?
| Gardening | Hiking | |
|---|---|---|
| Young Professionals | 15 | 10 |
| Retirees | 5 | 8 |
Step-by-Step Answer:
Calculate the total number of residents who like hiking:
$10 \, (\text{young professionals}) + 8 \, (\text{retirees}) = 18$
Calculate the total number of residents:
$15 \, (\text{young professionals}) + 10 \, (\text{young professionals hiking}) + 5 \, (\text{retirees}) + 8 \, (\text{retirees hiking}) = 38$
Calculate the percentage of residents who like hiking:
$\frac{\text{Total residents who like hiking}}{\text{Total residents}} \times 100 = \frac{18}{38} \times 100 \approx 47.37\%$
Therefore, the percentage of residents who like hiking is approximately $(47.37\%)$.
Percentage Calculation Table Of Values Question 8:
Q: In a technology survey, participants were asked to choose between using smartphones and laptops. The results are tabulated below. Determine the percentage of participants whose favorite device is a laptop?
| Smartphones | Laptops | |
|---|---|---|
| Students | 18 | 12 |
| Professionals | 15 | 20 |
Step-by-Step Answer:
Calculate the total number of participants:
$18 \text{(students)} + 12 \text{(students laptops)} + 15 \text{(professionals)} + 20 \text{(professionals laptops)}$.
Calculate the percentage of participants who like laptops.
$\text{Total Participants Liking Laptops} = 12 (\text{students}) + 20 (\text{professionals}) = 32$
$\text{Total Participants} = 18 (\text{students}) + 12 (\text{students laptops}) + 15 (\text{professionals}) + 20 (\text{professionals laptops}) = 65$
$\text{Percentage of Participants Liking Laptops} = \left( \frac{32}{65} \right) \times 100$
$\text{Percentage of Participants Liking Laptops} \approx 49.23\%$
Therefore, approximately 49.23% of the participants prefer laptops.
Percentage Calculation Table Of Values Question 9:
Q: In a survey of weekend activities, individuals were asked to choose between going to the movies and attending concerts. The results are tabulated below. Determine the percentage of individuals whose favorite weekend activity is attending concerts?
| Movies | Concerts | |
|---|---|---|
| Teenagers | 12 | 8 |
| Adults | 15 | 20 |
Step-by-Step Answer:
Calculate the percentage of individuals who like attending concerts.
Now, let’s proceed with the calculations:
$\text{Total Individuals Liking Concerts} = 8 (\text{teenagers}) + 20 (\text{adults}) = 28$
$\text{Total Individuals} = 12 (\text{teenagers}) + 8 (\text{teenagers concerts}) + 15 (\text{adults}) + 20 (\text{adults concerts}= 55$
$\text{Percentage of Individuals Liking Concerts} = \left( \frac{28}{55} \right) \times 100 $
$\text{Percentage of Individuals Liking Concerts} \approx 50.91\% $
Therefore, approximately 50.91% of the individuals prefer attending concerts.
Percentage Calculation Table Of Values Question 10:
Q: In a study of leisure activities, participants were asked to choose between reading books and watching TV. The results are tabulated below. Find the percentage of participants whose favorite activity is reading books?
| Reading Books | Watching TV | |
|---|---|---|
| College Students | 18 | 12 |
| Working Adults | 10 | 15 |
Certainly! Let’s complete the step-by-step answer:
Step-by-Step Answer (Continued):
Calculate the percentage of participants who like reading books.
Now, let’s proceed with the calculations:
$\text{Total Participants Liking Reading Books} = 18 (\text{college students}) + 10 (\text{working adults}) = 28$
$\text{Total Participants} = 18 (\text{college students}) + 12 (\text{college students watching TV}) + 10 (\text{working adults}) + 15 (\text{working adults watching TV}) = 55$
$\text{Percentage of Participants Liking Reading Books} = \left( \frac{28}{55} \right) \times 100$
$\text{Percentage of Participants Liking Reading Books} \approx 50.91\%$
Therefore, approximately 50.91% of the participants prefer reading books.
FAQs
Calculating a percentage involves finding a ratio of a part to a whole, expressed as a fraction of 100.
The general formula for calculating a percentage is:
Percentage=(Part/Whole)×100
“Percentage” and “percent” are terms that are often used interchangeably, and they both refer to a proportion or a ratio expressed as a fraction of 100. However, there is a subtle difference in their usage.
Percentage: “Percentage” is a noun. It refers to a specific number or ratio expressed as a fraction of 100.
For example: “The percentage of students who passed the exam was 75%.”
Percent: “Percent” is used as a noun when referring to ratios or proportions, and as an adjective when describing something in relation to a hundred.
For example: “She received a grade of 90 percent.”
(Here, “percent” is used as a noun.)
“The percent increase in sales was significant.”
(Here, “percent” is used as an adjective.)