1. **Problem Statement:** Given various percentages, ratios, quantities, and time periods, we need to solve problems related to interest, mixtures, profit/loss, and time. 2. **Formulas and Rules:** - Simple Interest (SI) = $\frac{P \times R \times T}{100}$ where $P$ is principal, $R$ is rate, $T$ is time. - Profit or Loss Percentage = $\frac{\text{Profit or Loss}}{\text{Cost Price}} \times 100$. - Mixture problems use ratios to find quantities or profit. - Time to multiply principal by a factor under simple interest: $T = \frac{(\text{Factor} - 1) \times 100}{R}$. 3. **Step-by-step Solutions:** **a. Time to become 8 times original principal:** - Using formula $T = \frac{(8 - 1) \times 100}{R}$. - Given $T = 15$ years, solve for $R$ or verify time. **b. Original Principal Calculation:** - Given total amount and interest, use $P = \frac{\text{Amount}}{1 + \frac{R \times T}{100}}$. - Example: $P = 4583.33$. **c. Profit on Milk Mixture:** - Profit = Selling Price - Cost Price. - Given profit = 45. **d. Overall Loss Percentage:** - Loss % = 4%. 4. **Explanation:** - Percentages represent rates or parts of quantities. - Ratios help divide quantities proportionally. - Fractions represent parts of whole quantities. - Time calculations relate to how long money or quantities change under given rates. 5. **Summary:** - Time to become 8 times original = 15 years. - Original principal = 4583.33. - Profit on milk mixture = 45. - Overall loss percentage = 4%.