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Buying is the gaining of an object in exchange for money, whereas selling is acquiring money in exchange of abandoning all claims ofownership from an object. Buying and selling are two terms that areoften used relatively whenever we are talking about buying and selling.Buying and selling are two sides of a coin. When one sells something,someone else buys it.

Buying is defined as acquiring the possession of, the right to, by payingor promising to pay its equivalence, especially in money.

The cost price is essentially the final price at which the seller buys the product or service. They then include a certain percentage of profit to it. The marked price or list price is the price that a seller establishes after including the necessary percentage of profit.

Symbols to be used

● CP stands for cost price

● SP stands for selling price

● Pr stands for profit

● CP= Cost Price

● CP= selling price - profit=SP-Pr

● Cost price = selling price - profit,

● CP= SP - Pr

Selling is defined as a transfer of goods or services in exchange for money.

Selling price is actually the price that a buyer pays in order to obtain a

product or service. Selling price is usually higher than the cost price

or alternatively, it is the cost price plus profit. Setting a selling price is

a very sensitive matter as the sales of a product are based on it.

The basic formula to find the selling price is:

Selling price = Cost price + Profit

In short

SP = CP + Pr

Calculating selling price, cost price and profit.

Example 1

A cycle was bought for $ 1235 and sold at a gain of $ 100. Find the selling price of the cycle.

Solution

Given

CP = $1235, Profit = $ 100, SP =?

SP = CP + Profit

SP = $ 1235 + $ 100 = $ 1335.

Discount is deduction in price. Discounts are often given for paying in cash. For instance, when a shop advertises a sale, they often give a standard discount on all goods, such as 25% discount oof every item in the store.

Some times the goods are advertised as marked down by 25%.

This means that every item will have its purchase price reduced by 25% or, equivalenty, the new price of the item will be 75% of the orginal price.

New pirce = Original price - Discount

New price = 100% of original price - 25% of original price = 75% of Original price.

Discount = Original price - new price

If a r% discount is applied then discount = r/100×original price.

New price = original price - discount

Selling price = (100-r)/100×original

Percentage discount = discount/marked price × 100%

Marked price = ( selling price )+( discount).

Note: marked price =original price, selling price= cash price

Example 1

If the cost of a book is decreased from $25 to $20, what percentage of reduction has been implemented?

Solution

Discount=original price - new price

= 25.00-20.00=$5.00

Percentage discount= discount/marked price×100%

Percentage discount= 5/25×100%=20%

A decimal number can be described as a numeral whose integer part and the fractional part are separated by a dot.

The dot in a decimal number is called a decimal point. The digits after the decimal point show a value smaller than one.

         Converting fractions into decimal numbers

Toconvert a proper fraction ( denominator is greater than the numerator ) into decimal number perform the ordinary division process by dividing the numerator by the denominator, the result will be a decimal point, as shown below.

Fraction form Decimal form

  1/2                                  0.5

  1/4                                  0.25

  3/10                                0.3       

  1/5                                  0.2

  6/10                                0.6

            Converting  decimal numbers into fractions

To change a decimal number into a fraction, look the number of digits at the rightof the decimal point, for :

1) 1 digit only remove the decimal point and divide the number by 10.

2) 2 digits remove the decimal point and divide the number by 100

3) 3 digits remove the decimal point and divide the number by 1000.

Profit, which is also called net income, is the amount of earningsthe exceed expenses in a given period of time. In other words, profit is a financial gain from business activity during a period of time.

Loss is the opposite of profit. It occurs when cost price is greater then selling price.

Profit an Loss Formulas

Cost price : The price at which an item is purchased.

Selling price : The price at which an item is sold.

Profit = Selling price - cost price

Loss = Cost price - Selling price

Example 1

If a product is bought at $400 and sold at $500. Calculate the profit.

Solution

Given

SP = $500 

CP= $400

Profit = ?

Profit = SP - CP

           = $500 - $400 

           = $100

Definition

A number is called a real number , if and only if it is either a rational number or an irrational number. The set of real numbers, denoted by R, canbe described as the union of the sets of rational and irrational numbers.

R = ( x : x is a rational number or an irrational number. )

R = Q ∪  “Q prime” where rational numbers ( Q ) and irrational numbers ( “Q prime” ) Subsets of real numbers

All real numbers except complex numbers are real numbers. 

Therefore, real numbers have the following five subsets :