 ## How to solve percent problems?

How many of you are aware that the word percent is derived from the Latin phrase "per centum"? Also, if you break down the word "percent" into the two words "per" and "cent," the meaning becomes pretty clear: it refers to $$100$$. As a result, we can conclude that percentages are nothing more than fractions whose denominators are always the number $$100$$.
So, we can say that in case of a percentage, $$100$$ is considered as the whole quantity. For example, if there are $$25\%$$ apples in a fruit shop, then that means that out of every $$100$$ fruits in that shop, $$25$$ are apples. It can also be used as a ratio like $$25:100$$. Also, in fraction form, it would be denoted as $$\frac{25}{100}$$ .

### Calculation of Percentage

Now that we know what is percentage, let’s find out how to calculate it with ease. In percentage problems, we basically have to find the part/share of a whole in terms of $$100$$. This we can do in the following 2 ways.

• Firstly, we can apply the unitary method.
• Secondly, we take the fraction in consideration and change its denominator to $$100$$.

A thing to note is that the second method can only be effectively used when the denominator of the fraction is a factor of $$100$$. If this isn’t the case, we will always resort to the first method.
Now, there is a very interesting formula to calculate the part, whole, and percentage.
This goes as $$part \ = \ \frac{percent}{100} \times whole$$
So, suppose in some numerical, you are asked to find out the separate entities like part or percent or even whole, then you can resort to this formula to find the individual answers.

### Percent Problems

To solve percent problems, you must remember the concept of three crucial things: Base, Part, and Percent.

• $$Base \ = \ Part \div Percent$$
• $$Part \ = \ Base \times Percent$$
• $$Percent \ = \ Part \div Base$$

Ex: $$3$$ is $$10\%$$ of $$30$$
Here, $$3$$ is the part, $$30$$ is the base, and $$10\%$$ is the percent, Now, if we put all these values in the above three equations, we can see that all of them hold true. Also, while verifying, use $$0.10$$ in the equation instead of $$10\%$$.

### Exercises for Percent Problems

1) $$\frac{64}{448} = \frac{x}{100}$$$$\ \Rightarrow \$$

2) $$\frac{78}{624} = \frac{x}{100}$$$$\ \Rightarrow \$$

3) $$\frac{14.28}{96} = \frac{x}{100}$$$$\ \Rightarrow \$$

4) $$\frac{33.33}{66} = \frac{x}{100}$$$$\ \Rightarrow \$$

5) $$\frac{10}{68} = \frac{x}{100}$$$$\ \Rightarrow \$$

6) $$\frac{10}{82} = \frac{x}{100}$$$$\ \Rightarrow \$$

7) $$\frac{94}{846} = \frac{x}{100}$$$$\ \Rightarrow \$$

8) $$\frac{80}{160} = \frac{x}{100}$$$$\ \Rightarrow \$$

9) $$\frac{66}{198} = \frac{x}{100}$$$$\ \Rightarrow \$$

10) $$\frac{96}{960} = \frac{x}{100}$$$$\ \Rightarrow \$$

1) $$\frac{64}{448} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{64}{448} \times 100 \ = 14.28}$$
2) $$\frac{78}{624} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{78}{624} \times 100 \ = 12.5}$$
3) $$\frac{14.28}{96} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{14.28}{96} \times 100 \ = 14.87}$$
4) $$\frac{33.33}{66} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{33.33}{66} \times 100 \ = 50.5}$$
5) $$\frac{10}{68} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{10}{68} \times 100 \ = 14.7}$$
6) $$\frac{10}{82} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{10}{82} \times 100 \ = 12.19}$$
7) $$\frac{94}{846} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{94}{846} \times 100 \ = 11.11}$$
8) $$\frac{80}{160} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{80}{160} \times 100 \ = 50}$$
9) $$\frac{66}{198} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{66}{198} \times 100 \ = 33.33}$$
10) $$\frac{96}{960} = \frac{x}{100}$$$$\ \Rightarrow \ \color{red}{x=\frac{96}{960} \times 100 \ = 10}$$

## Percent Problems Practice Quiz

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