How to Solve Percentage Problems with Examples? - BYJUS

# Solving Problems Based on Percentage

Percent is an alternate method of representing fractions and decimals. Here we will learn different methods of calculating the percent and the steps involved in each method. We will also look at some examples that will help you gain a better understanding of the concept....Read MoreRead Less

## What is meant by percentage?

In mathematics, a percentage is a number or ratio that represents a fraction of 100. The symbol “%” is frequently used to represent it, and it has a few hundred years of history. While we are on the topic of percentages, one example will be, the decimal 0.35, or the fraction $$\frac{7}{20}$$, which is equivalent to 35 percent, or 35%.

## Solving Problems Based on Percentages

By solving problems based on percentages, we can find the missing values and find the values of various unknowns in a given problem.

## Finding the percentage of a number

Find 40% of 200.

$$\frac{40}{100}\times 200$$             Write the percentage as a fraction

$$\frac{2}{5}\times 200=800$$           Simplify

## Finding the whole number from the percent

First, write the percentage as a fraction or decimal. Then, divide the fraction or decimal by the part. This method applies to any situation in which a percentage and its value are given.

If 2 percent equals 80, multiply 80 by 100 and divide it by 2 to get 4000.

Prove that 20% of 120 is 24.

20% =$$\frac{20}{100}$$      Write the percent as a fraction or decimal.

Using multiplication equation:

$$\frac{20}{100}\times 120=24$$     Simplify

To prove the reverse of this solution we use the  division equation:

$$\frac{24}{\frac{20}{100}}$$     Simplify

$$\frac{2400}{20}=120$$

## Finding the whole using the ratio method

A ratio table is the table that shows the comparison between two units and shows the relationship between them.

## Solved Examples

Example 1: What is 25% of 50?

Solution:

We have 25% of 50.

So, 25% of 50 = $$\frac{1}{4}\times 50$$ Write the percentage as a fraction or decimal.

= $$\frac{50}{4}$$    Simplify.

= 12.5

Example 2: Using the ratio table, answer the following question:

What is 60% of 200?

Solution:

We have 60% of 200.

Now, we have to use the ratio table to find the part. Let one row represent the part and the other row represent the whole row in the table and find the equivalent ratio of 200.

The first column represents the percentage = $$\frac{60}{100}$$

So, 60% of 200 is 120.

Example 3:Find the whole of the number.

50% of what number is 45.

Solution:

We have: 50% of what number is 45?

Use division equation

$$\frac{45}{50%}$$    Write the percentage as a fraction or decimal

$$=\frac{45}{\frac{1}{2}}$$  Simplify

So, $$45\times 2=90$$

Hence, 50% of 90 is 45

Example 4: Find the whole of the number using the ratio table.

140% of what number is 84

Solution:

We have to find 140% of what number is 84.

Use the ratio table to find the part. Let one be the part and the other be the whole row in the table. Now, find the equivalent ratio of 200.

So, 140% of 60 is 84.

Example 5: A rectangular hall’s width is 60 percent of its length.

What are the room’s dimensions?

Solution:

Calculate the width of the room by taking 60% of 15 feet.

$$60%\times 15$$ Write the percentage as a fraction or decimal.

= $$0.6\times 15$$     Simplify

= 9

We can also understand it with the help of a diagram:

The width is 9 feet.

Area of the rectangle = $$\text{length}\times \text{width}$$

= $$15\times 9$$

= 135

Hence, the area of the given room is 135 $$feet^2$$.

Example 6: You have won a camping trip at an auction at your school fair that cost $80. Your bid is 40% of your maximum bid for the price of the camping trip. How much more would you be willing to pay for the trip if you hadn’t already paid the full price? Solution: You are given the winning camping bid that represents the maximum bid as well as the percentage of your maximum bid. You must calculate how much more you would have paid for the camping trip if you had known how much more you were willing to pay. Your winning bid is the part, and your maximum bid is the whole. Create a model based on the fact that 40% of the total is$80 to determine the highest bid. Then divide the winning bid by the maximum bid to find out how much more you were willing to pay.

The maximum bid is $200 and the winning bid is$80. So, you would be willing to bid $200 –$80 = \$120 more for the tickets.

In mathematics, a percentage is a number or ratio that represents a fraction of 100 in mathematics. Percentage is usually represented by the symbol “%”. It is also written simply as “percent” or “pct”. For example, the decimal 0.35, or the fraction $$\frac{35}{100}$$, is equivalent to 0.35.