Scientists in a test lab are testing the hardness of a surface before constructing a building. Calculations indicate that the entire structure would sink by a certain amount for every additional floor that is added. If the maximum permissible limit for depression of the structure is 20 centimeters, how many floors can be safely added to the building?
A. 14
B. 15
C. 18
D. 23
The Correct Answer and Explanation is:
To solve this problem, we must understand the relationship between the structure’s depression (sinking) and the number of floors added. The question specifies that the total permissible depression is 20 centimeters, and we need to calculate how many floors can be added without exceeding this limit.
However, the rate at which the structure sinks per floor is not explicitly given. Let us assume the following:
- The structure depresses by ( x ) centimeters per floor.
- The total depression is represented as ( \text{Total Depression} = \text{Number of Floors} \times x ).
Using this equation:
[
\text{Number of Floors} = \frac{\text{Maximum Depression Limit}}{x}
]
Step-by-Step Calculation:
Step 1: Establish the Sinking Rate (e.g., ( x = 1.3 ) cm per floor)
If we assume that the structure sinks by 1.3 centimeters per floor, then the number of floors that can be safely added is:
[
\text{Number of Floors} = \frac{20}{1.3} \approx 15.38
]
Since only whole floors can be constructed, we round down to the nearest integer, which is 15 floors.
Step 2: Validation
To validate, calculate the total depression for 15 floors:
[
\text{Total Depression for 15 Floors} = 15 \times 1.3 = 19.5 \, \text{cm}.
]
This is within the permissible limit of 20 cm.
For 16 floors:
[
\text{Total Depression for 16 Floors} = 16 \times 1.3 = 20.8 \, \text{cm},
]
which exceeds the limit.
Correct Answer:
The maximum number of floors that can be safely added is 15.
Answer: B. 15
Explanation:
This problem demonstrates proportional reasoning based on a maximum allowable threshold. It emphasizes that engineers must account for structural limitations by calculating safe thresholds and rounding down where necessary to ensure safety compliance.