The dimensions of a room are $12.5\text{ metres}$ by $9\text{ metres}$ by $7\text{ metres}$. There are $2$ doors and $4$ windows in the room; each door measures $2.5\text{ metres}$ by $1.2\text{ metres}$ and each window $1.5\text{ metres}$ by $1\text{ metre}$. Find the cost of painting the walls at ₹ $3.50$ per square metre.

### Concept & Effective Paintable Area When painting a room, doors and windows are typically excluded. To find the effective paintable area, subtract their total area from the total area of the four walls. $$ \text{Paintable Area} = 2(l + b)h - (\text{Area of Doors} + \text{Area of Windows}) $$ ### Step-by-Step Solution * Identify the dimensions of the room: $l = 12.5\text{ m}$, $b = 9\text{ m}$, $h = 7\text{ m}$. * Calculate the total area of the four walls: $2(12.5 + 9) \times 7 = 2(21.5) \times 7 = 43 \times 7 = 301 \text{ m}^2$. * Calculate the area of the 2 doors: $2 \times (2.5 \times 1.2) = 2 \times 3 = 6 \text{ m}^2$. * Calculate the area of the 4 windows: $4 \times (1.5 \times 1) = 4 \times 1.5 = 6 \text{ m}^2$. * Find the total unpaintable area: $6 + 6 = 12 \text{ m}^2$. * Determine the effective paintable area: $301 - 12 = 289 \text{ m}^2$. * Multiply by the rate to find total cost: $289 \times 3.50$. * Cost = $289 \times (7/2) = 2023 / 2 = \text{₹ } 1011.50$. ### Exam Strategy & Shortcut Using fractions for monetary rates can save time. Converting ₹ $3.50$ to $7/2$ makes multiplying with $289$ cleaner, avoiding decimal multiplication errors when solving manually under time pressure. ### Common Pitfall A common error is skipping the multiplication by the number of doors ($2$) or windows ($4$) and simply subtracting the area of a single door and window from the total wall area. ### Final Answer Therefore, the correct answer is **₹ 1011.50**.