- 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 \(5\%\),

\(=200-10\)

\(=$190\)

A \($30\)

B \($170\)

C \($230\)

D \($100\)

- 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.

A \(20\%\)

B \(15\%\)

C \(30\%\)

D \(25\%\)

- 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

\(=48.15×15\%\)

\(=48.15×0.15\)

\(=$7.2\)

A \($19.44\)

B \($18.44\)

C \($18\)

D \($20\)

- 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.

A \(9\%\)

B \(10\%\)

C \(8.2\%\)

D \(8\%\)

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.

A \($1,740\)

B \($1,520\)

C \($2,200\)

D \($1,680\)

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.

A \($2,040.00\)

B \($1,860.00\)

C \($3,160.00\)

D \($1,780.00\)