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: 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: Remaining salary after food and education** $$1 - \frac{7}{10} = \frac{3}{10}$$ 5. **Step 3: Fraction spent on travelling** Travelling is half of remaining: $$\frac{1}{2} \times \frac{3}{10} = \frac{3}{20}$$ 6. **Step 4: Remaining after travelling** $$\frac{3}{10} - \frac{3}{20} = \frac{6}{20} - \frac{3}{20} = \frac{3}{20}$$ 7. **Step 5: Fraction spent on other expenses** Other expenses are $\frac{2}{3}$ of remaining after travelling: $$\frac{2}{3} \times \frac{3}{20} = \frac{2}{20} = \frac{1}{10}$$ 8. **Step 6: Fraction saved** Total fractions spent: $$\frac{7}{10} + \frac{3}{20} + \frac{1}{10} = \frac{14}{20} + \frac{3}{20} + \frac{2}{20} = \frac{19}{20}$$ Savings fraction: $$1 - \frac{19}{20} = \frac{1}{20}$$ 9. **Step 7: Find total salary** Savings amount = $\frac{1}{20}$ of salary = 3250 So, $$\text{Salary} = 3250 \times 20 = 65000$$ **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