Informative line

Conversion Into Percents Circle Graphs

Percent Decrease

  • 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.

Illustration Questions

The original cost of a dress was \($150\). If it is now on sale for \($120\), what is the percent decrease in cost?

A \(20\%\)

B \(30\%\)

C \(40\%\)

D \(120\%\)

×

Given:

Original cost of dress \(=$150\)

Sale Price of dress \(=$120\)

Difference between the amount of original price and sale price

\(=$150-$120\)

\(=$30\)

Amount of decrease in price \(=$30\)

Original Price \(=$150\)

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

\(\Rightarrow\text {Percent decrease} = \dfrac{30}{150}\) or \(\dfrac {1}{5}\)

Converting the fraction into a percent by using proportion.

\(\Rightarrow\dfrac {1}{5}=\dfrac {x}{100}\)

Solve by using the cross multiplication method:

image

\(\Rightarrow5x=1×100\)

\(\Rightarrow5x=100\)

\(\Rightarrow x=\dfrac {100}{5}\)

\(\Rightarrow x=20\)

Thus, the cost of dress decreases by \(20\%\).

Hence, option (A) is correct.

The original cost of a dress was \($150\). If it is now on sale for \($120\), what is the percent decrease in cost?

A

\(20\%\)

.

B

\(30\%\)

C

\(40\%\)

D

\(120\%\)

Option A is Correct

Finding New Amount Using Percent of Change

  • 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

Illustration Questions

Alex bought a pair of shoes for \($40\). His friend bought the same pair of shoes at \(20\%\) less than that of Alex. Calculate the cost price of Alex's friend's shoes.

A \($34\)

B \($32\)

C \($36\)

D \($38\)

×

Given:

Cost of Alex's Shoes \(=$40\)

Now, calculating the cost of Alex's friend's shoes.

Amount of Change = Percent of Change × Original Amount

\(=20\%×40\)

Amount of change \(=20\%×40\)

\(=0.20×40\)

\(=$8\)

Since there is a decrease, so subtract the amount of change from the price and calculate the cost price of Alex's friend's shoes.

Thus, the cost price of Alex's friend's shoes

\(=$40-$8\)

\(=$32\)

Hence, option (B) is correct.

Alex bought a pair of shoes for \($40\). His friend bought the same pair of shoes at \(20\%\) less than that of Alex. Calculate the cost price of Alex's friend's shoes.

A

\($34\)

.

B

\($32\)

C

\($36\)

D

\($38\)

Option B is Correct

Finding New Amount using Percent of Change-II

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.

Illustration Questions

Two friends, Aron and Keith work in the same company. Aron is getting \($3,500\) per month while Keith earns \(120\%\) of what Aron earns. Calculate how much Keith earns.

A \($3,620\)

B \($600\)

C \($4,200\)

D \($4,000\)

×

Given:

Total income of Aron \(=$3,500\) per month

Calculating the income of Keith,

New Amount = Percent of Change × Original Amount

\(=120\%×3,500\)

\(=\dfrac {120}{100}×3,500\)

\(=1.20×3,500\)

\(=$4,200\)

Thus, the income of Keith is \($4,200\).

Hence, option (C) is correct.

 

 

Two friends, Aron and Keith work in the same company. Aron is getting \($3,500\) per month while Keith earns \(120\%\) of what Aron earns. Calculate how much Keith earns.

A

\($3,620\)

.

B

\($600\)

C

\($4,200\)

D

\($4,000\)

Option C is Correct

Percent Increase

  • 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 \(46.6\%\).

Illustration Questions

In the first year, Sam saves \($5,100\). Next year he saves  \($5,406\). By what percent has Sam's savings increased in the second year?

A \(5\%\)

B \(8\%\)

C \(7\%\)

D \(6\%\)

×

Given:

Total savings in the first year \(=$5,100\)

Total savings in the second year \(=$5,406\)

Difference between the savings of \(2\) years

\(=$5406-$5100\)

\(=$306\)

Increase in savings (Amount of Increase) \(=$306\)

Savings in the first year (Original Amount) \(=$5,100\)

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

\(\Rightarrow\text {Percent Increase}=\dfrac {306}{5,100}\) or \(\dfrac {51}{850}\)

Now, converting the fraction into a percent by using proportion,

\(\dfrac {51}{850}=\dfrac {x}{100}\)

Solve by using the cross multiplication method:

image

\(\Rightarrow850x=51×100\)

\(\Rightarrow850x=5100\)

\(\Rightarrow x=\dfrac {5100}{850}\)

\(\Rightarrow x=6\)

Thus, the savings have increased by \(6\%\).

Hence, option (D) is correct.

In the first year, Sam saves \($5,100\). Next year he saves  \($5,406\). By what percent has Sam's savings increased in the second year?

A

\(5\%\)

.

B

\(8\%\)

C

\(7\%\)

D

\(6\%\)

Option D is Correct

Circle Graphs (Interpretation)

  • 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.

Illustration Questions

The circle graph represents the percentage of students having different weights in a class. Which statement is FALSE? (Weight is in pounds)

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

Option (A):

We can observe the following from the circle graph:

Percentage of students belonging  to \(68-70\) pounds category\(=32\%\)

Percentage of students belonging to \(66-68\) pounds category \(=16\%\)

Since, \(32=2×16\)

Hence, option (A) is true.

Option (B):

According to the circle graph,

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

Hence, option (B) is true.

Option (C):

The percentage of students belonging to \(64-66\) pounds weight category \(=10\%\)

The percentage of students belonging to \(70-72\) pounds weight category \(=20\%\)

Since, \(10\%=\dfrac {20\%}{2}\)

Hence, option (C) is true.

Option (D): 

The percentage of students belonging to \(64-66\) pounds weight category is \(10\%\).

Hence, option (D) is FALSE.

The circle graph represents the percentage of students having different weights in a class. Which statement is FALSE? (Weight is in pounds)

image
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 \(9\%\).

Option D is Correct

Percent through Circle Graph-II 

  • 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.

Illustration Questions

James starts a business of fruit selling. The circle graph represents the percentage of different types of fruits he has for selling. If there are a total of \(600\) fruits to sell, find how many apples are there?

A \(146\)

B \(132\)

C \(360\)

D \(115\)

×

Total number of fruits \(=600\)

From the circle graph,

Apples \(=22\text {%}\)

Number of apples \(=22\text {% of }\,600\)

\(=.22×600\)

\(=132\)

Hence, option (B) is correct.

James starts a business of fruit selling. The circle graph represents the percentage of different types of fruits he has for selling. If there are a total of \(600\) fruits to sell, find how many apples are there?

image
A

\(146\)

.

B

\(132\)

C

\(360\)

D

\(115\)

Option B is Correct

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