A plot of land in the form of a rectangle has dimensions $240 \text{ m} \times 180 \text{ m}$. A drainlet $10 \text{ m}$ wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by $25 \text{ cm}$. The depth of the drainlet is

### Concept & Formula The volume of the earth dug from the drainlet equals the volume of the earth spread over the plot. $$ \text{Volume of earth} = \text{Area of plot} \times \text{Increase in height} $$ $$ \text{Volume of drainlet} = \text{Area of drainlet} \times \text{Depth} $$ ### Step-by-Step Solution 1. **Find the area of the plot:** $\text{Plot Area} = 240 \times 180 = 43200 \text{ m}^2$ 2. **Find the volume of earth spread:** $\text{Rise} = 25 \text{ cm} = 0.25 \text{ m}$ $\text{Volume spread} = 43200 \times 0.25 = 10800 \text{ m}^3$ 3. **Find the area of the outer drainlet:** Outer dimensions $= (240 + 10 + 10) \times (180 + 10 + 10) = 260 \text{ m} \times 200 \text{ m}$ $\text{Outer Area} = 52000 \text{ m}^2$ $\text{Drainlet Area} = \text{Outer Area} - \text{Plot Area} = 52000 - 43200 = 8800 \text{ m}^2$ 4. **Equate volumes to find the depth ($d$):** $8800 \times d = 10800$ $d = \frac{10800}{8800} = \frac{108}{88} = \frac{27}{22} \approx 1.2272... \text{ m}$ ### Exam Strategy & Shortcut Instead of calculating huge areas, calculate the drainlet area using the formula: $2w(L+B+2w)$, where $w$ is width. $2(10)(240+180+20) = 20(440) = 8800$. Equate $8800 \times d = 43200 \times 0.25$ directly. ### Common Pitfall Forgetting to add twice the width of the path ($10+10=20$) to both the length and the breadth when calculating the outer area. ### Final Answer Therefore, the correct answer is **1.227 m**.