Commercial Mathematics - Percentage and its applications

Definition of Percentage: The term 'Percentage' is derived from the Latin 'per centum', meaning 'per hundred'. It is a way of expressing a part of a whole as a fraction with a denominator of 100, denoted by the symbol $\%$. Visually, imagine a $10 \times 10$ square grid representing 100 units; if 35 squares are colored, they represent $35\%$ of the grid.

Conversion Rules: To convert a fraction or decimal into a percentage, multiply the number by 100 and suffix the $\%$ sign. Conversely, to convert a percentage into a fraction or decimal, divide the number by 100 and remove the $\%$ sign. Think of this as shifting a decimal point two places to the right (for conversion to percentage) or two places to the left (for conversion from percentage).

Profit and Loss: In commercial math, Cost Price ($CP$) is the price at which an article is bought, and Selling Price ($SP$) is the price at which it is sold. If $SP > CP$, it is a Profit; if $CP > SP$, it is a Loss. Visually, this can be seen as a bar graph where the difference in height between the $SP$ and $CP$ bars represents either the profit (if $SP$ is higher) or the loss (if $CP$ is higher).

Overhead Expenses: Overheads include additional costs like transportation, labor, or repair costs incurred after purchasing an item. These are always added to the original Cost Price to get the 'Total Cost Price'. All subsequent profit or loss calculations are based on this Total Cost Price. For example, if you buy a second-hand cycle and pay for new tires, your total investment is the purchase price plus the tire cost.

Profit and Loss Percentages: These are the profit or loss values expressed as a percentage of the Cost Price. They allow for a standardized comparison of financial performance regardless of the actual money involved. A $10\%$ profit means that for every 100 units of currency spent, 10 units are gained as profit.

Simple Interest: This is the interest calculated only on the principal amount ($P$) for a specific time period ($T$) at a fixed rate of interest ($R$). Visually, Simple Interest represents linear growth on a timeline, where the amount of interest added remains constant for every equal interval of time (e.g., every year).

Amount: The total money returned at the end of a loan or investment period is called the Amount ($A$). It is the sum of the original Principal and the Simple Interest earned ($A = P + SI$). On a growth chart, the Principal is the starting value on the y-axis, and the Amount is the final value reached after time $T$.