1. **Problem statement:** (a) Given the assessed annual value of a house is 20000 and the municipal council charges 8% as rates per annum. Monthly rent is 12000. (i) Find the annual rates to be paid. (ii) Find the tax amount paid quarterly. (iii) Given maintenance cost is 38000 per annum, find total income per annum. (b) A TV is imported with 3% tax on its value. After tax, the value is 51500. (i) Find the value before tax. (ii) Find the tax amount paid. 2. **Formulas and rules:** - Tax or rates amount = assessed value \times rate percentage - Quarterly tax = annual tax \div 4 - Total income = annual rent - (annual rates + maintenance cost) - Value after tax = original value + tax amount - Tax amount = original value \times tax rate 3. **Calculations:** (a)(i) Annual rates = $20000 \times \frac{8}{100} = 1600$ (a)(ii) Quarterly tax = $\frac{1600}{4} = 400$ (a)(iii) Annual rent = $12000 \times 12 = 144000$ Total expenses = rates + maintenance = $1600 + 38000 = 39600$ Total income = $144000 - 39600 = 104400$ (b)(i) Let original value be $x$ Value after tax = $x + 0.03x = 1.03x = 51500$ Solve for $x$: $$ \cancel{1.03}x = \frac{51500}{\cancel{1.03}} = 50000 $$ (b)(ii) Tax amount = $51500 - 50000 = 1500$ **Final answers:** (a)(i) Rs. 1600 (a)(ii) Rs. 400 (a)(iii) Rs. 104400 (b)(i) Rs. 50000 (b)(ii) Rs. 1500