Confidential information - This is for official consumption \( \begin{array}{l}\text { I use } \frac{1}{12} \text { of my salary to pay for rates and taxes, } \frac{1}{16} \text { to pay for insurance and } \frac{5}{6} \\ \text { to meet other expenses. If I have R320 left of my monthly salary, calculate my } \\ \text { yearly salary. }\end{array} \)

To solve this puzzle, let's denote your monthly salary as \( S \). According to your distribution of expenses: 1. Rates and taxes: \( \frac{1}{12} S \) 2. Insurance: \( \frac{1}{16} S \) 3. Other expenses: \( \frac{5}{6} S \) These must add up to the total salary minus the amount left (R320): \[ S - \left( \frac{1}{12}S + \frac{1}{16}S + \frac{5}{6} S \right) = 320 \] To simplify the left-hand side, first find a common denominator for the fractions (which is 48): - \( \frac{1}{12} S = \frac{4}{48} S \) - \( \frac{1}{16} S = \frac{3}{48} S \) - \( \frac{5}{6} S = \frac{40}{48} S \) Now, substituting these into the equation gives: \[ S - \left( \frac{4}{48} S + \frac{3}{48} S + \frac{40}{48} S \right) = 320 \] Combine the fractions: \[ S - \frac{47}{48} S = 320 \] This simplifies to: \[ \frac{1}{48} S = 320 \] Now, multiply both sides by 48 to find \( S \): \[ S = 320 \times 48 = 15360 \] So, your monthly salary is R15,360. To find the yearly salary, multiply by 12: \[ \text{Yearly Salary} = 15,360 \times 12 = R184,320 \] Your yearly salary is R184,320!