100 men took a dip in a water tank 50 m long and 20 m wide. If the average displacement of water by a man is 5 m³, then what is the rise in the water level?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The total volume of water displaced is the product of the number of men and the average displacement per man: 100 men × 5 m³ = 500 m³.
The surface area of the water in the rectangular tank is its length multiplied by its width: 50 m × 20 m = 1000 m².
The rise in water level (height) is found by dividing the total displaced volume by the surface area of the tank: 500 m³ / 1000 m² = 0.5 meters.
To match the units in the options, the result is converted from meters to centimeters: 0.5 m × 100 cm/m = 50 cm.

Option A: A rise of 75 cm (0.75 m) would mean a displaced volume of 1000 m² × 0.75 m = 750 m³. This is incorrect as only 500 m³ was displaced.
Option C: A rise of 60 cm (0.60 m) would require a displaced volume of 1000 m² × 0.60 m = 600 m³, which is greater than the actual displaced volume of 500 m³.
Option D: A rise of 40 cm (0.40 m) corresponds to a displaced volume of 1000 m² × 0.40 m = 400 m³. This is less than the actual displaced volume of 500 m³.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of volume and its effect on water level in a container as background academic context rather than a clinical decision trigger.
This question assesses fundamental mathematical reasoning, a skill crucial for accurate nursing calculations like medication dosage, IV drip rates, and fluid balance monitoring.
The underlying principle of volume displacement is analogous to clinical concepts such as edema, where excess fluid accumulates in tissues, or ascites, the buildup of fluid in the abdomen.
What if? If the tank was 40 m long and 20 m wide (Area = 800 m²), the rise in water level would be 500 m³ / 800 m² = 0.625 m, or 62.5 cm.

How to Approach the Question

First, identify all the numerical values given in the problem: number of men (100), tank dimensions (50 m length, 20 m width), and average displacement per man (5 m³).
Next, determine the objective: to find the rise in the water level.
Calculate the total volume of water displaced by multiplying the number of men by the displacement per man.
Calculate the surface area of the water in the tank using the formula: Area = Length × Width.
The rise in water level is the total displaced volume divided by the surface area. This gives the height in meters.
Finally, check the units of the options. Convert your answer from meters to centimeters (1 m = 100 cm) to match the options.

Concept Tested & Keywords

Concept Tested: Calculation of volume and its effect on water level in a container.
Stem keywords: men, water tank, long, wide, displacement, rise in water level
Lead-in keywords: what is

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