1. **State the problem:** Rosila spent $\frac{1}{8}$ of her salary on transport and then $\frac{1}{3}$ of the remainder on food. After these expenses, she had 840 left. We need to find her total salary. 2. **Define variables:** Let Rosila's salary be $S$. 3. **Calculate amount spent on transport:** She spent $\frac{1}{8}S$ on transport. 4. **Calculate remainder after transport:** The remainder is $S - \frac{1}{8}S = \frac{7}{8}S$. 5. **Calculate amount spent on food:** She spent $\frac{1}{3}$ of the remainder on food, which is $\frac{1}{3} \times \frac{7}{8}S = \frac{7}{24}S$. 6. **Calculate remainder after food:** The amount left after food is the remainder minus food expenses: $$\frac{7}{8}S - \frac{7}{24}S = \frac{21}{24}S - \frac{7}{24}S = \frac{14}{24}S = \frac{7}{12}S$$ 7. **Set up equation with amount left:** We know this remainder equals 840: $$\frac{7}{12}S = 840$$ 8. **Solve for $S$:** Multiply both sides by $\cancel{\frac{12}{7}} \times \frac{7}{12}$ to isolate $S$: $$S = 840 \times \frac{12}{7}$$ 9. **Simplify:** $$S = 840 \times \frac{12}{7} = 840 \times \frac{12}{7} = 840 \times \frac{12}{7}$$ First simplify $\frac{12}{7}$: $$\frac{12}{7} = 1.7142857...$$ Or better to simplify by dividing 840 by 7: $$840 \div 7 = 120$$ Then multiply by 12: $$120 \times 12 = 1440$$ 10. **Final answer:** Rosila's salary is $\boxed{1440}$.