Final answer:
After subtracting the 20m² gap area from the total 120m² floor area, we're left with 100m² to place chairs that each cover 1.5m². This calculation shows that a maximum of 66 chairs can fit, but this number does not match the provided options, suggesting an error in the question.
Step-by-step explanation:
To find the maximum number of chairs that can be kept in the room, we must first subtract the total space of the gap between the chairs from the total area of the floor. After that, we will divide the remaining space by the area covered by one chair to find out how many chairs can fit in the remaining space.
The total area of the floor is 120m². The gap between the chairs covers 20m², and each chair covers 1.5m² of space. First, we calculate the area available for chairs:
Total area of floor - Area of gaps = Available area for chairs
120m² - 20m² = 100m²
Now, to find out the number of chairs:
Available area for chairs ÷ Area covered by one chair = Number of chairs
100m² ÷ 1.5m² = 66.66, which means a maximum of 66 chairs (since we cannot have a fraction of a chair).
Therefore, none of the options (a) 72, (b) 64, (c) 80, (d) 56 is correct. If those were the only options, perhaps there is a mistake in the question or the options provided, as the calculation suggests a different outcome. It might be best to clarify with the instructor or source of the question.