1. **Problem statement:** A bank manager spends fractions of his salary on various expenses and saves 3250. We need to find fractions spent on food and education, travelling, other expenses, savings, and his total salary. 2. **Given:** - Food = $\frac{2}{5}$ of salary - Children's education = $\frac{3}{10}$ of salary - Remaining after food and education = $1 - \left(\frac{2}{5} + \frac{3}{10}\right)$ - Travelling = $\frac{1}{2}$ of remaining - Other expenses = $\frac{2}{3}$ of remaining after travelling - Savings = 3250 3. **Step 1: Calculate fraction spent on food and education** $$\frac{2}{5} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}$$ So, fraction spent on food and education = $\frac{7}{10}$ 4. **Step 2: Calculate remaining salary after food and education** $$1 - \frac{7}{10} = \frac{3}{10}$$ 5. **Step 3: Calculate fraction spent on travelling** Travelling = $\frac{1}{2}$ of remaining = $\frac{1}{2} \times \frac{3}{10} = \frac{3}{20}$ 6. **Step 4: Calculate remaining after travelling** $$\frac{3}{10} - \frac{3}{20} = \frac{6}{20} - \frac{3}{20} = \frac{3}{20}$$ 7. **Step 5: Calculate fraction spent on other expenses** Other expenses = $\frac{2}{3}$ of remaining after travelling = $\frac{2}{3} \times \frac{3}{20} = \frac{2}{20} = \frac{1}{10}$ 8. **Step 6: Calculate fraction saved** Total spent = food + education + travelling + other expenses $$= \frac{7}{10} + \frac{3}{20} + \frac{1}{10} = \frac{14}{20} + \frac{3}{20} + \frac{2}{20} = \frac{19}{20}$$ Savings fraction = $1 - \frac{19}{20} = \frac{1}{20}$ 9. **Step 7: Calculate total salary** Savings amount = $\frac{1}{20}$ of salary = 3250 So, salary = $3250 \times 20 = 65000$ **Final answers:** - i. Fraction spent on food and education = $\frac{7}{10}$ - ii. Fraction spent on travelling = $\frac{3}{20}$ - iii. Fraction spent on other expenses = $\frac{1}{10}$ - iv. Fraction saved = $\frac{1}{20}$ - v. Monthly salary = 65000