A rectangular tank is 25 m long, 12 m wide and 6 m deep. If its walls and bottom are to be plastered at the rate of 75 paise per sq. m, what will be the total cost of plastering?

Introduction / Context:
This mensuration question deals with the surface area of a rectangular tank and the cost of plastering that surface. It checks whether you can correctly identify which surfaces need to be plastered and then compute the total cost using a given rate per unit area. Such real life cost calculation problems are frequently used in exams to test practical application of geometry.

Given Data / Assumptions:

- Length of the tank = 25 m.
- Width of the tank = 12 m.
- Depth (or height) of the tank = 6 m.
- Plastering is to be done on the four vertical walls and the horizontal bottom only.
- Rate of plastering = 75 paise per sq. m, that is Rs. 0.75 per sq. m.

Concept / Approach:
The total plastered area is the sum of the areas of the four walls and the bottom. For a rectangular tank, opposite walls have equal areas. Once total area in square metres is found, multiply it by the cost per square metre to obtain the total expenditure. No plastering is done on the open top surface, so it is not included in the calculation.

Step-by-Step Solution:
Step 1: Area of the bottom = length * width = 25 * 12 = 300 sq. m.Step 2: There are two walls of size 25 m by 6 m each. Combined area of these two walls = 2 * (25 * 6) = 2 * 150 = 300 sq. m.Step 3: The other two walls are 12 m by 6 m each. Combined area of these walls = 2 * (12 * 6) = 2 * 72 = 144 sq. m.Step 4: Total plastered area = bottom area + area of all four walls = 300 + 300 + 144 = 744 sq. m.Step 5: Rate of plastering = Rs. 0.75 per sq. m.Step 6: Total cost = 744 * 0.75.Step 7: 744 * 0.75 = 744 * 3 / 4 = 558, so the total cost is Rs. 558.

Verification / Alternative check:
You can quickly verify by checking individual wall areas again: two large walls contribute 300 sq. m, two smaller walls add 144 sq. m and the base adds another 300 sq. m, confirming 744 sq. m. Multiplying by 0.75 can also be checked by first finding 75 percent of 744, which is indeed 558, because 50 percent is 372 and 25 percent is 186, and 372 + 186 = 558.

Why Other Options Are Wrong:
Rs. 456 and Rs. 502 are obtained if parts of the surface are mistakenly omitted or if the rate is applied incorrectly. Rs. 600 and Rs. 744 result from using the wrong rate or incorrectly taking one full rupee instead of 75 paise per sq. m or confusing area with perimeter. None of these match the correct combined effect of both area and rate.

Common Pitfalls:
Students often forget that the top surface is open and should not be plastered, while the bottom must be included. Another mistake is to add only one wall of each type instead of both equal walls, which halves their contribution. Finally, misinterpreting 75 paise as Rs. 75 or Rs. 1 can cause large numerical errors. Carefully reading the units and surfaces involved prevents such mistakes.

Final Answer:
Hence, the total cost of plastering the tank is Rs. 558.