- Percent decrease refers to the ratio or proportion of the amount of decrease to the original amount/quantity.
- We can find the percent decrease by using the following steps:

**Step 1: **Find the amount of decrease by subtracting the new amount from the original amount.

Amount of decrease = Original Amount – New Amount

**Step 2: **Write a fraction in which, take the amount of decrease as the numerator and the original amount as the denominator.

\(\text {Percent Decrease}=\dfrac {\text{Amount of decrease}}{\text {Original Amount}}\)

**Step 3: **Write an equivalent fraction with \(x\) as the numerator and \(100\) as the denominator.

\(\dfrac {\text{Amount of decrease}}{\text{Original amount}}=\dfrac {x}{100}\)

**Step 4: **Solve the equation using cross multiplication method.

**Example: **In the month of June, the average temperature of a city was \(32°C\) while in October, it dropped to \(16°C\). What is the percent decrease in temperature?

Average temperature in June \(=32°C\)

Average temperature in October \(=16°C\)

- Difference / Decrease in temperature

\(=32°C-16°C\)

\(=16°C\)

- \(\text {Percent Decrease}=\dfrac {\text{Difference in temperature}}{\text {Original temperature}}\)

\(=\dfrac {16°C}{32°C}\)

\(=\dfrac {1}{2}\)

** **Write an equivalent fraction with \(x\) as the numerator and \(100\) as the denominator.

\(\dfrac {\text{Amount of decrease}}{\text{Original amount}}=\dfrac {x}{100}\)

\(\Rightarrow\dfrac {1}{2}=\dfrac {x}{100}\)

Solve by using cross multiplication method:

\(\Rightarrow\;2x=1×100\)

\(\Rightarrow\;2x=100\)

\(\Rightarrow\;x=\dfrac {100}{2}\)

\(\Rightarrow\;x=50\)

Thus, the temperature decreases by \(50\%\) in October.

A \(20\%\)

B \(30\%\)

C \(40\%\)

D \(120\%\)

- If percent increase or percent decrease and the original amount are given, then we can find the new amount.
- Find the new amount by using the following formula:

**Amount of Change = Percent of Change × Original Amount**

To calculate the new amount:

(i) In case of increase

**New Amount = Original Amount + Amount of Change**

(ii) In case of decrease

**New Amount = Original Amount – Amount of Change**

Let's consider an example to understand how to calculate the new amount using percent of change.

**Example: **Carl got \(30\) marks in Physics. After revaluation, his marks increased by \(10\%\), now what are his marks in Physics after revaluation?

Change in Marks = Percent of Change × Original Marks

\(=10\%×30\)

\(=\dfrac {10}{100}×30\)

\(=0.1×30\)

\(=3\)

Since there is an increase, so add the change in marks to the original marks to calculate the revalued marks.

Thus, Carl now scored

\(=30+3=33\) marks

If the percent of change is above \(100\%\) then we calculate the new amount by using the following formula:** **

**New Amount = Percent of Change × Original Amount**

- Let's consider an example to understand how to calculate new amount using the percent of change.

From a sports store, Alex bought a football for \($25\). His friend bought a similar football from a different store for \(140\%\) of what Alex paid.

How much money did Alex's friend spend?

New Amount = Percent of Change × Original Amount

\(=140\%×25\)

\(=\dfrac {140}{100}×25\)

\(=1.40×25\)

\(=$35\)

Hence, Alex's friend spent \($35\) on the football.

A \($3,620\)

B \($600\)

C \($4,200\)

D \($4,000\)

- Percent increase refers to the ratio of the amount of increase in a quantity to the original amount of quantity.
- We can find the percent increase by using the following steps:

**Step 1: **Find the amount of increase by subtracting the original amount from the new amount.

**Amount of increase = New Amount – Original Amount**

**Step 2: **Write a fraction in which, take the amount of increase as the numerator and the original amount as the denominator.

\(\text {Percent Increase}=\dfrac {\text{Amount of Increase}}{\text{Original Amount}}\)

**Step 3: **Write an equivalent fraction with \(x\) as the numerator and \(100\) as the denominator.

\(\dfrac {\text{Amount of Increase}}{\text{Original amount}}=\dfrac {x}{100}\)

**Step 4: **Solve the equation using cross multiplication method.

**Example: ** The cost of each pen increases from \($0.15\) to \($0.22\). Find what percent increase is there in the cost of a single pen?

- The original cost of a pen \(=$0.15\)

The cost increases to \($0.22\)

- Difference / Increase in cost \(=$0.22-$0.15\)

\(=$0.07\)

- \(\text {Percent Increase}=\dfrac {\text{Difference in Cost}}{\text{Original Cost}}\)

\(\dfrac {$0.07}{$0.15}=\dfrac {$7}{$15}\)

Write an equivalent fraction with \(x\) as the numerator and \(100\) as the denominator.

\(\dfrac {\text{Difference in Cost}}{\text{Original Cost}}=\dfrac {x}{100}\)

Solve by using the cross multiplication method:

\(\Rightarrow\;15x=7×100\)

\(\Rightarrow\;15x=700\)

\(\Rightarrow\;x=\dfrac {700}{15}\)

\(\Rightarrow\;x=46.6\%\)

Thus, the cost of a pen increases by \(46.6\%\).

A \(5\%\)

B \(8\%\)

C \(7\%\)

D \(6\%\)

- A circle graph is a way of displaying the data.
- A circle represents the whole i.e. \(100\%\).
- It is divided into parts known as sections.
- Each section looks like a pie-shaped wedge.
- Each pie-shaped wedge represents a percent of the whole.

**Example: **

The given circle graph represents the percentage of the population in a state under different age groups.

A percent represents the part of a whole and a circle represents the \(100\%\).

The given circle graph is divided into \(5\) parts known as sections. On observing the above circle graph, we have:

Population of \(0-20\) age group \(=30\%\)

Population of \(20-40\) age group \(=33\%\)

Population of \(40-60\) age group \(=24\%\)

Population of \(60-70\) age group \(=7\%\)

Population of \(70\) and above age group \(=6\%\)

We can observe -

- The highest percentage is \(33\%\) which is the age group of \(20-40\) years.
- The least percentage is \(6\%\) which is the age group of \(70\) and above.
- The percentage of \(40-60\) age group is \(4\) times of the percentage of \(70\) and above, i.e. \(24=4×6\)
- The percentage of \(0-20\) age group is \(5\) times of the percentage of \(70\) and above, i.e. \(30=5×6\)
- The percentage of \(40-60\) age group is higher than the percentage of \(60-70\) age group.

A The percentage of students belonging to \(68-70\) pounds weight category is twice the percentage of students belonging to \(66-68\) pounds weight category.

B The percentage of students belonging to \(72-74\) pounds weight category is \(13\%\).

C The percentage of students belonging to \(64-66\) pounds weight category is half the percentage of students belonging to \(70-72\) pounds weight category.

D The percentage of students belonging to \(64-66\) pounds weight category is \(9\%\).

- A circle graph is a way of displaying data.
- A full circle represents the \(100\text{%}\).
- It is divided into a number of sections, known as pie shaped wedges.
- Each wedge represents a percent of the whole.

**Let us consider the following example:**

Here, the circle represents the percentage of students that play different sports, at a school.

The total number of students is \(200\).

Now the question is....... "How many students play baseball, cricket and basketball?"

We can calculate it by using the concept of "Percent of a number".

Thus, the number of students who play

**Baseball = **\(50\text {% of }200\)

\(=.50×200=100\)

**Cricket = \(20\text {% of }200\)**

**\(=.20×200=40\)**

**Basketball = \(30\text {% of }200\)**

**\(=.30×200=60\)**

This means, ** \(100\)** students play Baseball, \(40\) students play Cricket, and \(60\) students play Basketball.