1. The problem is to understand and compare quantities, a key concept in Class 8 NCERT math. 2. Comparing quantities involves finding the ratio or difference between two or more quantities to understand their relationship. 3. Important formulas and concepts: - Ratio: $$\text{Ratio} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$$ - Percentage: $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$$ - Difference: $$\text{Difference} = |\text{Quantity 1} - \text{Quantity 2}|$$ 4. Logical problems often involve applying these formulas to real-life scenarios, such as comparing prices, speeds, or quantities. 5. Example problem: Compare 150 and 200. - Step 1: Find the ratio: $$\frac{150}{200} = \frac{3}{4}$$ - Step 2: Find the difference: $$200 - 150 = 50$$ - Step 3: Find the percentage of 150 with respect to 200: $$\left(\frac{150}{200}\right) \times 100 = 75\%$$ 6. Explanation: The ratio 3:4 means for every 3 units of the first quantity, there are 4 units of the second. The difference 50 shows how much one quantity exceeds the other. The percentage 75% means 150 is 75% of 200. 7. These methods help in comparing quantities logically and quantitatively. This is a fundamental skill in math and daily life for making informed decisions.