1. **State the problem:** Devi spent fractions of her money on lunch and a book, then used the remainder to buy a poster costing 60 more than the book. We need to find the initial amount of money she had. 2. **Define variables:** Let the initial amount of money be $x$. 3. **Calculate money spent on lunch:** She spent $\frac{1}{6}x$ on lunch. 4. **Calculate remainder after lunch:** Remaining money is $x - \frac{1}{6}x = \frac{5}{6}x$. 5. **Calculate money spent on book:** She spent $\frac{1}{3}$ of the remainder on the book, so book cost is $\frac{1}{3} \times \frac{5}{6}x = \frac{5}{18}x$. 6. **Calculate remainder after book:** Remaining money is $\frac{5}{6}x - \frac{5}{18}x = \frac{15}{18}x - \frac{5}{18}x = \frac{10}{18}x = \frac{5}{9}x$. 7. **Poster cost:** The poster costs $60$ more than the book, so poster cost is $\frac{5}{18}x + 60$. 8. **Set remainder equal to poster cost:** The remainder after buying the book is used to buy the poster, so $$\frac{5}{9}x = \frac{5}{18}x + 60$$ 9. **Solve for $x$:** Multiply both sides by 18 to clear denominators: $$18 \times \frac{5}{9}x = 18 \times \left(\frac{5}{18}x + 60\right)$$ $$10x = 5x + 1080$$ Subtract $5x$ from both sides: $$10x - 5x = 1080$$ $$5x = 1080$$ Divide both sides by 5: $$x = \frac{1080}{5} = 216$$ 10. **Answer:** Devi initially had 216. **Final answer:** 216