U4 Percentages (I) Essential Formulas

This section covers the fundamental concepts of percentages, including percentage change, profit and loss, and simple interest. Mastery of these formulas is crucial for solving real-world financial and quantitative problems in the DSE exam.

1 Percentage Change

Percentage Increase / Decrease

The percentage change is calculated by comparing the difference between the new value and the original value to the original value. A positive result indicates an increase, while a negative result indicates a decrease.

$$ \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\% $$
OriginalNewChange

2 Profit and Loss

Profit / Loss Percentage

Profit or loss is expressed as a percentage of the cost price. Profit occurs when the selling price $S$ is greater than the cost price $C$, and loss occurs when $S$ is less than $C$.

$$ \text{Profit Percentage} = \frac{S - C}{C} \times 100\% $$
$$ \text{Loss Percentage} = \frac{C - S}{C} \times 100\% $$

Selling Price Formula

The selling price can be found if the cost price and the profit/loss percentage are known.

$$ S = C \times (1 + r\%) $$

where $r\%$ is the profit percentage (positive) or loss percentage (negative).

3 Simple Interest

Interest and Total Amount

Simple interest is calculated only on the principal amount $P$ for a period of $T$ years at an annual interest rate of $R\%$. The interest earned is not reinvested.

$$ I = P \times \frac{R}{100} \times T $$
$$ A = P + I = P \left(1 + \frac{R}{100} \times T \right) $$

where $I$ is the simple interest and $A$ is the total amount.

4 Finding Original Value

Reverse Calculation

Given the new value after a percentage increase or decrease, the original value can be found by reversing the operation.

$$ \text{Original Value} = \frac{\text{New Value}}{1 + r\%} $$

where $r\%$ is the percentage change (use $+$ for increase, $-$ for decrease).

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