1. The problem is to understand and compare quantities using formulas typically taught in class 8. 2. When comparing quantities, we often use ratios and percentages to express how one quantity relates to another. 3. The basic formula for ratio is: $$\text{Ratio} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$$ This tells us how many times one quantity contains another. 4. To express a quantity as a percentage of another, use: $$\text{Percentage} = \left(\frac{\text{Quantity 1}}{\text{Quantity 2}}\right) \times 100\%$$ This converts the ratio into a percent form. 5. Important rules: - Ratios compare two quantities of the same kind. - Percentages express parts per hundred. - Always simplify ratios to their lowest terms. 6. Example: If Quantity 1 is 50 and Quantity 2 is 200, - Ratio = $$\frac{50}{200} = \frac{1}{4}$$ - Percentage = $$\frac{50}{200} \times 100 = 25\%$$ 7. This means Quantity 1 is one-fourth or 25% of Quantity 2. This is how you compare quantities using formulas in class 8 math.