A tank is 20 m long, 15 m wide and 10 m deep. What is the cost of plastering its walls and bottom at 80 paise per sq m?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The area to be plastered includes the four walls and the bottom of the tank.
The area of the four walls (lateral surface area) is calculated as 2 × (Length + Width) × Height, which is 2 × (20 + 15) × 10 = 700 m².
The area of the bottom is Length × Width, which is 20 × 15 = 300 m².
The total area to be plastered is the sum of the wall area and bottom area: 700 + 300 = 1000 m².
The cost is 80 paise (or Rs 0.80) per m². The total cost is 1000 m² × Rs 0.80/m² = Rs 800.

Option A: Rs. 200 is a significant underestimation of the cost. This result would likely stem from a major error in calculating the surface area, such as only considering a small portion of the tank or making a large arithmetic mistake.
Option B: Rs. 400 is exactly half of the correct answer. This error could occur if one calculates the total area correctly (1000 m²) but then mistakenly halves the cost rate (to 40 paise or Rs 0.40) before multiplying.
Option C: Rs. 600 is incorrect. This value is close to the cost of plastering only the walls (700 m² × Rs 0.80 = Rs 560). A student might arrive at this by forgetting to include the area of the tank's bottom in the total area calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to calculate the surface area of a cuboid (specifically, an open-top tank) and apply a unit cost to find the total cost as background academic context rather than a clinical decision trigger.
While not a clinical question, this problem assesses basic numeracy and problem-solving skills, which are essential for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance monitoring, all of which require accuracy and a clear understanding of units and formulas.
What if the tank also had a top to be plastered? In that case, you would add another bottom area (300 m²) to the total, making the total area 1300 m², and the cost would be 1300 × 0.80 = Rs 1040.

How to Approach the Question

First, carefully read the question to identify all the given information: the dimensions of the tank (length, width, depth) and the cost rate for plastering.
Identify what needs to be calculated: the cost of plastering the 'walls and bottom'. This tells you the tank is open at the top.
Break the problem into smaller parts: calculate the area of the walls, calculate the area of the bottom, and then sum them to get the total area.
Use the correct formula for the area of the walls (lateral surface area): 2 × (L+W) × H.
Use the correct formula for the area of the bottom: L × W.
Finally, multiply the total area by the cost per square meter. Remember to convert paise to rupees if necessary to match the options.

Concept Tested & Keywords

Concept Tested: This question tests the ability to calculate the surface area of a cuboid (specifically, an open-top tank) and apply a unit cost to find the total cost.
Stem keywords: tank, long, wide, deep, cost, plastering, walls, bottom
Lead-in keywords: What is

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Practise the full DSSSB -28 August 2019 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.