| Category | Concept / Formula |
| Basic Definition | $x\% = \frac{x}{100}$ |
| Fraction to Percent | $\frac{a}{b} = \left( \frac{a}{b} \times 100 \right)\%$ |
| Price Increase | If price increases by $R\%$, reduction in consumption to keep expenditure same: $\left[ \frac{R}{(100 + R)} \times 100 \right]\%$ |
| Price Decrease | If price decreases by $R\%$, increase in consumption to keep expenditure same: $\left[ \frac{R}{(100 – R)} \times 100 \right]\%$ |
| Population Growth | Population after $n$ years: $P \left( 1 + \frac{R}{100} \right)^n$ Population $n$ years ago: $\frac{P}{\left( 1 + \frac{R}{100} \right)^n}$ |
| Depreciation | Value after $n$ years: $P \left( 1 – \frac{R}{100} \right)^n$ Value $n$ years ago: $\frac{P}{\left( 1 – \frac{R}{100} \right)^n}$ |
| Comparison (More Than) | If $A$ is $R\%$ more than $B$, then $B$ is less than $A$ by: $\left[ \frac{R}{(100 + R)} \times 100 \right]\%$ |
| Comparison (Less Than) | If $A$ is $R\%$ less than $B$, then $B$ is more than $A$ by: $\left[ \frac{R}{(100 – R)} \times 100 \right]\%$ |
Aptitude: Percentage Formula Reference
| Category | Concept / Formula |
| Basic Definition | $x\% = \frac{x}{100}$ |
| Fraction to Percent | $\frac{a}{b} = \left( \frac{a}{b} \times 100 \right)\%$ |
| Price Increase | If price increases by $R\%$, reduction in consumption to keep expenditure same: $\left[ \frac{R}{(100 + R)} \times 100 \right]\%$ |
| Price Decrease | If price decreases by $R\%$, increase in consumption to keep expenditure same: $\left[ \frac{R}{(100 – R)} \times 100 \right]\%$ |
| Population Growth | Population after $n$ years: $P \left( 1 + \frac{R}{100} \right)^n$ Population $n$ years ago: $\frac{P}{\left( 1 + \frac{R}{100} \right)^n}$ |
| Depreciation | Value after $n$ years: $P \left( 1 – \frac{R}{100} \right)^n$ Value $n$ years ago: $\frac{P}{\left( 1 – \frac{R}{100} \right)^n}$ |
| Comparison (More Than) | If $A$ is $R\%$ more than $B$, then $B$ is less than $A$ by: $\left[ \frac{R}{(100 + R)} \times 100 \right]\%$ |
| Comparison (Less Than) | If $A$ is $R\%$ less than $B$, then $B$ is more than $A$ by: $\left[ \frac{R}{(100 – R)} \times 100 \right]\%$ |
Key Takeaways
- Population/Depreciation: These formulas use the principle of compound interest. Note the plus sign for growth and the minus sign for depreciation.
- Inverse Relationships: When calculating how much one value must change to compensate for another (like price vs. consumption), the denominator adjusts based on whether the initial change was an increase $(100 + R)$ or a decrease $(100 – R)$.
