Informative line

Applications Of Percent

Calculation of Discount

Discount 

  • Discount is an offer to the customers to pay less than the original price.
  • It is the amount of money which is taken away or not to be paid from the original price.
  • It is usually in the form of a percent.

Example: \(10\%\) discount or discount of \(10\%\)

  • It can be represented by the word 'off' too.
  • The discount offer is a marketing strategy that promotes business.
  • It induces the customers to shop and helps the business to increase its sales and clear the old stock.

Use the following formula to calculate the amount of discount.

Amount of discount = Percent of discount × Original amount

For example:

If there is a \(5\%\) discount on the original price of \(\$200\), we can calculate the amount of discount as:

Percent of discount \(=5\%\)

Original amount \(=$200\)

Amount of discount \(=\) Percent of discount × original amount 

\(=5\%×200\)

\(=\dfrac {5}{100}×200\)

\(=0.05×200\)

\(=10\)

Thus, amount of discount \(=$10\)

Subtract the amount of discount from the original amount to calculate the new amount after discount.

Therefore, new amount after the discount of \(5\%\),

\(=200-10\)

\(=$190\)

Illustration Questions

Julie wants to purchase a bicycle. The original price of the bicycle is \($200\). If there is a \(15\%\) discount, how much money will she pay to purchase the bicycle?

A \($30\)

B \($170\)

C \($230\)

D \($100\)

×

Given:

Original price of bicycle \(=$200\)

Percent of discount \(=15\%\)

We know that,

Amount of discount = Percent of discount × Original amount

By putting the given values in the formula, we get:

Amount of discount 

\(=15\%×200\)

\(=\dfrac {15}{100}×200\)

\(=0.15×200\)

\(=$30\)

Now, subtracting the amount of discount from the original amount to calculate the new amount after discount,

\(=200-30\)

\(=170\)

Thus, Julie will pay \($170\) to purchase the bicycle.

Hence, option (B) is correct.

Julie wants to purchase a bicycle. The original price of the bicycle is \($200\). If there is a \(15\%\) discount, how much money will she pay to purchase the bicycle?

A

\($30\)

.

B

\($170\)

C

\($230\)

D

\($100\)

Option B is Correct

Percent of Discount

  • Discount is the amount of money which is taken away or not to be paid from the original price.
  • It is usually in the form of a percent.
  • We can calculate the percent of discount by solving the given proportion below:

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

where \(x=\) Percent of discount

For example: 

Cody spends \($72\) for two shirts at a clothing store. If the original price of the two shirts was \($80\) then the percent of discount can be calculated as follows:

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

\(\Rightarrow\dfrac {80-72}{80}=\dfrac {x}{100}\)

\(80x=8×100\)

\(80x=800\)

\(x=\dfrac {800}{80}=10\%\)

Thus, there was \(10\%\) discount on the original price of shirts.

Illustration Questions

Alex bought headphones on sale for \($30\). If the original price of the headphones was \($40\), find the percent of discount on the headphones.

A \(20\%\)

B \(15\%\)

C \(30\%\)

D \(25\%\)

×

Given:

Original price of headphones \(=$40\)

Cost of headphones after discount \(=$30\)

We know that

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

where \(x=\) Percent of discount.

By putting the given values in the proportion, we get:

\(\dfrac {40-30}{40}=\dfrac {x}{100}\)

\(\Rightarrow\dfrac {10}{40}=\dfrac {x}{100}\)

\(\Rightarrow\;40x=100×10\)

\(\Rightarrow\;40x=1000\)

\(\Rightarrow\;x=25\%\)

Thus, the percent of discount on the headphones was \(25\%\) .

Hence, option (D) is correct.

Alex bought headphones on sale for \($30\). If the original price of the headphones was \($40\), find the percent of discount on the headphones.

A

\(20\%\)

.

B

\(15\%\)

C

\(30\%\)

D

\(25\%\)

Option D is Correct

Calculation of Sales Tax and Tip

  • Sales tax and Tip, both are opposites of discount.
  • Sales tax is a tax paid on goods and services purchased and is generally an extra percentage of money added to the buyer's cost.
  • A tip is an extra amount of money which is given by the customer to the person providing services. Example: Tip to a waiter, tip to a driver etc.
  • A tip is a gratuity.
  • Markup is the term used for profit. It is the difference between original amount and selling price.

Example: Original amount = \($100\)

Selling price \(=$120\)

\(\therefore\) Mark up = Selling price – Original amount

\(=$120-$100\)

\(=$20\)

\($20\) is the profit of the seller.

  • For discount, we subtract an amount from the original amount while for sales tax and tip, we add an amount to the original amount.
  • By using the following formula, we can find the amount of sales tax or tip.
  •  Amount of tax = Original amount × Percent of tax
  • Then, add the amount of sales tax or tip to the original amount.

For Example:

Alex and his family had dinner at a restaurant. The waiter presented the bill of \($45\) excluding sales tax of \(7\%\). Alex's father paid \(15\%\) of the total bill (including sales tax) as a tip to the waiter.

Calculate the amount of tip and Sales tax.

Percent of tax \(=7\%\)

Percent of tip \(=15\%\)

Original amount of dinner \(=$45\)

Amount of tax = Original amount × Percent of tax

\(=45×7\%\)

\(=45×0.07\)

\(= $3.15\)

Thus, the total bill including sales tax

\(=45+3.15=$48.15\)

Amount of tip = Amount including tax × Percent of tip

\(=48.15×15\%\)

\(=48.15×0.15\)

\(=$7.2\)

Illustration Questions

Jacob goes to a store to buy a pair of trousers. The cost of a pair of trousers is \($18\) without sales tax. If the sales tax rate is \(8\%\), how much will he pay for the purchase?

A \($19.44\)

B \($18.44\)

C \($18\)

D \($20\)

×

Given:

Percent of Sales tax \(=8\%\)

Original cost of a pair of trousers \(=$18\)

Amount of tax = Original cost × Percent of tax

\(=18×8\%\)

\(=18×0.08\)

\(=$1.44\)

Now, we add the amount of tax to the original amount.

\(=$1.44+$18\)

\(=$19.44\)

Thus, Jacob will pay \($19.44\) to buy a pair of trousers.

Hence, option (A) is correct.

Jacob goes to a store to buy a pair of trousers. The cost of a pair of trousers is \($18\) without sales tax. If the sales tax rate is \(8\%\), how much will he pay for the purchase?

A

\($19.44\)

.

B

\($18.44\)

C

\($18\)

D

\($20\)

Option A is Correct

Percent of Sales Tax and Tip

  • Sales tax and Tip, both are opposites of discount.
  • Sales tax is a tax paid on goods and services purchased and is generally an extra percentage of money added to the buyer's cost.
  • A tip is an extra percentage amount of money which is given by the customer to the person providing services. Example: Tip to a waiter, tip to a driver etc.
  • A tip is a gratuity.
  • Markup is the term used for profit. It is the difference between original amount and selling price.

Example: Original amount = \($100\)

Selling price \(=$120\)

\(\therefore\) Mark up = Selling price – Original amount

\(=$120-$100\)

\(=$20\)

\($20\) is the profit of the seller.

  • For discount, we subtract an amount from the original amount while for sales tax and tip, we add an amount to the original amount.
  • By using the following formula, we can find the percent of sales tax or tip:

\(\text {Percent of Tax/Tip}=\dfrac {\text {Difference of Amount}}{\text {Original Amount}}=\dfrac {x}{100}\)

 

Then solve it by using cross multiplication method.

For Example:

Kara wants to tip her cab driver, so she gives \($17\) to him. If the cost of commuting is \($15\) then the percentage of the tip can be calculated as follows:

Total amount Kara pays \(=$17\)

Cab fare \(=$15\)

To find the percentage of the tip, we apply the formula:

\(\text {Percent of Tip}=\dfrac {\text {Difference of Amount}}{\text {Original Amount(fare)}}=\dfrac {x}{100}\)

\(\Rightarrow\dfrac {17-15}{15}=\dfrac {x}{100}\)

\(\Rightarrow\dfrac {2}{15}=\dfrac {x}{100}\)

Now, solve it by using cross multiplication method.

\(\Rightarrow\,15x=2×100\)

\(\Rightarrow\,15x=200\)

\(\Rightarrow\,x=\dfrac {200}{15}\)

\(x=13.3\%\)

Thus, Kara tipped at the rate of \(13.3\%\) to the cab driver.

Illustration Questions

Ms. Thompson paid a total of \($86.94\) for a tablet. If the original price of the tablet was \($80.5\), what percent of sales tax did Ms. Thompson pay?

A \(9\%\)

B \(10\%\)

C \(8.2\%\)

D \(8\%\)

×

Given:

Total amount paid by Ms. Thompson  \(=$86.94\)

Original amount of tablet \(=$80.5\)

To find the percent of tax, we apply the formula:

\(\text {Percent of Tax}=\dfrac {\text {Difference of Amount}}{\text {Original Amount}}=\dfrac {x}{100}\)

\(\Rightarrow \;\dfrac {86.94-80.5}{80.5}=\dfrac {x}{100}\)

\(\Rightarrow\dfrac {6.44}{80.5}=\dfrac {x}{100}\)

Solve by using cross multiplication method.

image

\(\Rightarrow80.5x=6.44×100\)

\(\Rightarrow80.5x=644\)

\(\Rightarrow x=\dfrac {644}{80.5}\)

\(\Rightarrow x=8\%\)

Thus, she paid \(8\%\)  as sales tax.

Hence, option (D) is correct.

Ms. Thompson paid a total of \($86.94\) for a tablet. If the original price of the tablet was \($80.5\), what percent of sales tax did Ms. Thompson pay?

A

\(9\%\)

.

B

\(10\%\)

C

\(8.2\%\)

D

\(8\%\)

Option D is Correct

Miscellaneous

Example: Kara has a \(16\) meters long cloth. She uses \(15\%\) cloth to sew a skirt and \(7.5\%\) to sew a shirt. After giving few meters long cloth to her sister, she is left with \(\dfrac {1}{8}\) of the original length. Find the length of the cloth that her sister receives.

 Total length of the cloth \(=16\) meters

Length of the cloth to sew a skirt

\(=16×15\%\)

\(=16×0.15\)

\(=2.4\) meters

Length of the cloth to sew a shirt

\(=16×7.5\)

\(=16×0.075\)

\(=1.2\) meters

Length of the cloth Kara is having at the end

\(=\dfrac {1}{8}×16\)

\(=2\) meters

\(\therefore\)  Length of the cloth she gives to her sister 

\(=16-(2.4+1.2+2)\)

\(=16-5.6\)

\(=10.4\) meters

Thus, she gives \(10.4\) meters long cloth to her sister.

Illustration Questions

Ms. Wendy earns \($3,500\) per month. She spends \(\dfrac {1}{5}\) of her salary on groceries, \(28\%\) on house rent, and \(\dfrac {1}{25}\) on the electricity bill. How much money does Ms. Wendy have now?

A \($1,740\)

B \($1,520\)

C \($2,200\)

D \($1,680\)

×

Given:

Monthly salary of Ms. Wendy \(=$3,500\)

Part of money spent by her:

On groceries \(=\dfrac{1}{5}\)

On house rent \(=28\%\)

On bills \(=\dfrac {1}{25}\)

First, convert all the numbers in the same form.

Converting \(\dfrac {1}{5}\) into percent,

image

\(5×x=100×1\)

\(5x=100\)

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

\(x=20\%\)

Converting \(\dfrac {1}{25}\) into percent,

image

\(25x=1×100\)

\(25x=100\)

\(x=\dfrac {100}{25}=4\%\)

Total percent of money Ms. Wendy spends:

\(20\%+4\%+28\%=52\%\)

\(52\%\) of \($3,500\) is

\(52\%=\dfrac {52}{100}\)

\(\dfrac {52}{100}=\dfrac {x}{3500}\)

\(100(x)=52×3500\)

\(x=\dfrac {52×3500}{100}\)

\(x=$1,820\)

Ms. Wendy spends \($1,820\).

She now has

\(=$3,500-$1,820=$1,680\)

Hence, option (D) is correct.

Ms. Wendy earns \($3,500\) per month. She spends \(\dfrac {1}{5}\) of her salary on groceries, \(28\%\) on house rent, and \(\dfrac {1}{25}\) on the electricity bill. How much money does Ms. Wendy have now?

A

\($1,740\)

.

B

\($1,520\)

C

\($2,200\)

D

\($1,680\)

Option D is Correct

Simple Interest

When we borrow an amount of money from a bank or a money lender for a certain period of time, we have to pay back some extra money along with the borrowed amount.

The extra money paid over and above the original amount is called simple interest.

To calculate it, we have to understand the following three terms:

Principal (P):  Amount of money borrowed/ loan amount

Rate (r): Rate of interest per year, generally in percentage form

Time(t): Time for which money is borrowed

Thus, Interest \((I)=P×r×t\)

\(=P\,r\,t\)

For example:  Mr. Craven wants to buy a car.

He takes a loan of \($10,000.00\) from a bank. The bank charges \(9\text{%}\) interest per year for \($10,000.00\). Here, the question arises,

"How much interest will he pay after \(4\) years?"

To determine the answer, we should calculate the interest, i.e. 

\(I=P\,r\,t\)

where 

\(P=\) Principal

\(r=\) Rate percent

\(t=\) Time taken

\(I=\) Interest

In the above example:

Principal = \($10,000.00\)

Rate = \(9\text{%}\)

Time = 4 years

\(I=$10,000.00×9\text{%}×4\) years (\(\because\;9\text{%}=0.09\))

\(I=10000×0.09×4\)

\(=40000×0.09\)

\(\begin{array} {r} 40000 \\ ×0.09 \\ \hline 3600.00\\ \hline \end{array}\)

\(I=$3,600.00\)

Thus, Mr. Craven will pay \($3,600\) as interest.

Illustration Questions

Mr. Wilson wants to buy a house. He takes a loan of \($8,500\) from a bank. If he has to return \(8\text{%}\) annually to the bank, how much money will he pay as simple interest in \(3\) years?

A \($2,040.00\)

B \($1,860.00\)

C \($3,160.00\)

D \($1,780.00\)

×

\(I=P\,r\,t\)

where 

\(P=\) Principal

\(r=\) Rate percent

\(t=\) Time taken

\(I=\) Interest

Principal is the amount borrowed.

Principal (P) = \($8,500.00\)

Rate (r) = \(8\text{%}\) per year

Time (t) = 3 years

Putting values in 

\(I=P\,r\,t\)

\(I=$8,500.00×8\text{%}×3\) years (\(\because\;8\text{%}=0.08\))

\(I=8500×0.08×3\)

\(=25500×0.08\)

\(\begin{array} {r} 25500 \\ ×0.08 \\ \hline 2040.00\\ \hline \end{array}\)

\(I=$2,040.00\)

Hence, option (A) is correct.

Mr. Wilson wants to buy a house. He takes a loan of \($8,500\) from a bank. If he has to return \(8\text{%}\) annually to the bank, how much money will he pay as simple interest in \(3\) years?

A

\($2,040.00\)

.

B

\($1,860.00\)

C

\($3,160.00\)

D

\($1,780.00\)

Option A is Correct

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