A rectangular tank has internal dimensions 25 m in length, 12 m in width and 6 m in depth. If only the four side walls and the bottom of the tank are to be plastered, calculate the total cost of plastering at the rate of 75 paise (Rs. 0.75) per square metre.

Introduction / Context:
This aptitude question is based on mensuration of three dimensional shapes, specifically a rectangular tank. The task is to find the cost of plastering only the internal walls and the bottom surface, given the internal dimensions and the plastering rate per square metre. Understanding how to compute total surface area of selected faces is the key concept here.

Given Data / Assumptions:

• Length of tank (L) = 25 m.
• Width of tank (W) = 12 m.
• Depth or height (H) = 6 m.
• Plastering is to be done on the four side walls and the bottom only, not on the top opening.
• Cost of plastering = Rs. 0.75 per sq m (75 paise per square metre).

Concept / Approach:
A rectangular tank is like a cuboid. The area to be plastered is the sum of the area of the bottom and the areas of the four vertical walls. The side walls form two pairs of equal rectangles. Once the total area is obtained, we multiply this area by the cost per square metre to obtain the total plastering cost. Careful separation of bottom and wall areas avoids overcounting.

Step-by-Step Solution:
Area of bottom = L * W = 25 * 12 = 300 sq m.Two longer walls each have area = L * H = 25 * 6 = 150 sq m, so together = 2 * 150 = 300 sq m.Two shorter walls each have area = W * H = 12 * 6 = 72 sq m, so together = 2 * 72 = 144 sq m.Total area to be plastered = bottom + four walls = 300 + 300 + 144 = 744 sq m.Cost per sq m = Rs. 0.75, so total cost = 744 * 0.75.Compute: 744 * 0.75 = 744 * 3 / 4 = 558.Therefore, total cost of plastering = Rs. 558.

Verification / Alternative check:
As a quick check, note that the total wall area is 444 sq m (300 + 144), and adding the bottom area 300 sq m gives 744 sq m. Multiplying by 0.75 can be checked by first finding three quarters of 700 (which is 525) and three quarters of 44 (which is 33), giving 525 + 33 = 558. This independently confirms the computed cost.

Why Other Options Are Wrong:
Rs. 458 and Rs. 608 come from using an incorrect total area such as missing one pair of walls or miscalculating the product 25 * 12. Rs. 658 and Rs. 758 are larger values that would imply an area greater than 744 sq m or an incorrect rate. None of these are consistent with the correct area and rate multiplication.

Common Pitfalls:
A common error is to include the top face of the tank, which is open and not to be plastered. Another mistake is to calculate the surface area of the whole cuboid and then forget to subtract the top. Students also sometimes convert 75 paise incorrectly; remembering that 75 paise equals Rs. 0.75 simplifies the multiplication. Always identify clearly which faces are to be covered before computing the area.

Final Answer:
Rs. 558