A tank is $25\text{ m}$ long, $12\text{ m}$ wide and $6\text{ m}$ deep. The cost of plastering its walls and bottom at $75\text{ paise}$ per sq. m, is

### Concept & Surface Area To plaster the walls and bottom of a tank, we need to calculate the lateral surface area (four walls) plus the area of the base, excluding the top. $$ \text{Total Plastering Area} = 2(l + b)h + lb $$ ### Step-by-Step Solution * Given dimensions: length $l = 25\text{ m}$, breadth $b = 12\text{ m}$, and depth $h = 6\text{ m}$. * Calculate the area of the four walls: $2(25 + 12) \times 6 = 2(37) \times 6 = 444 \text{ m}^2$. * Calculate the area of the bottom floor: $l \times b = 25 \times 12 = 300 \text{ m}^2$. * Total area to be plastered = $444 + 300 = 744 \text{ m}^2$. * The rate is given as $75\text{ paise}$ per square meter, which is equal to ₹ $0.75$ (or $3/4$ of a rupee). * Total cost = $\text{Total Area} \times \text{Rate} = 744 \times 0.75 = \text{₹ } 558$. ### Exam Strategy & Shortcut Instead of multiplying $744$ by $0.75$ directly, recognize that $0.75 = 3/4$. So, calculate $744 \times (3/4)$. $744 / 4 = 186$, and $186 \times 3 = 558$. This makes the mental math much faster. ### Common Pitfall Forgetting to include the bottom of the tank when calculating the total surface area to be plastered, or accidentally including the top surface (which is open). ### Final Answer Therefore, the correct answer is **₹ 558**.