1. **State the problem:** Kavitha saved money over three months to buy a laptop. She saved $\frac{1}{3}$ of the laptop's cost in the first month, $125$ less than that amount in the second month, and the remaining $525$ in the third month. We need to find the total cost of the laptop. 2. **Define variables:** Let the total cost of the laptop be $x$. 3. **Express savings:** - First month savings: $\frac{1}{3}x$ - Second month savings: $\frac{1}{3}x - 125$ - Third month savings: $525$ 4. **Set up the equation:** The sum of the savings over three months equals the total cost: $$\frac{1}{3}x + \left(\frac{1}{3}x - 125\right) + 525 = x$$ 5. **Simplify the equation:** $$\frac{1}{3}x + \frac{1}{3}x - 125 + 525 = x$$ $$\frac{2}{3}x + 400 = x$$ 6. **Isolate $x$:** $$x - \frac{2}{3}x = 400$$ $$\frac{1}{3}x = 400$$ 7. **Solve for $x$:** $$x = 400 \times 3 = 1200$$ **Final answer:** The laptop cost $1200$.