Question

A residential housing project is designed in a plot measuring 1 hectare. The car parking area is equally distributed between the ground floor and the basement. Considering the data given below, the number of cars accommodated in the basement will be \underline{\hspace{2cm}} [in integer]. Data: - FAR consumed = 2.0
- Car parking area is exempted from built up area for FAR calculations.
- One car parking to be given for each 100 sq.m of built up area.
- Area required for accommodating each car in ground floor = 15 sq.m
- Area required for accommodating each car in basement = 25 sq.m

Hint:

Be careful: In such parking problems, the area distribution is key, not directly the number of cars. Always compute total parking area, split equally, then divide by area requirement per car.

Answer 1

Step 1: Calculate plot area.
\n\[\n\text{Plot area} = 1 \; \text{hectare} = 10{,}000 \; \text{m}^2\n\] \n\n \n

Step 2: Determine built-up area using FAR.
\n\[\n\text{Built-up area} = FAR \times \text{Plot area} = 2.0 \times 10{,}000 = 20{,}000 \; \text{m}^2\n\] \n\n \n

Step 3: Calculate car parking requirement.
\nOne car parking space is required for every 100 sq.m of built-up area.
\n\[\n\text{Required parking spaces} = \frac{20{,}000}{100} = 200 \; \text{cars}\n\] \n\n \n

Step 4: Distribute parking between ground floor and basement.
\nParking is allocated equally: \n\[\n200 \div 2 = 100 \; \text{cars in ground floor (minimum allocation)}, 100 \; \text{cars in basement}\n\] \n\n \n

Step 5: Determine area requirements and adjust.
\n- Ground floor: Each car requires 15 sq.m.
\n\[\n100 \times 15 = 1500 \; \text{m}^2\n\] \n\n- Basement: Each car requires 25 sq.m. For 100 cars initially: \n\[\n100 \times 25 = 2500 \; \text{m}^2\n\] \n\nHowever, the parking area allocation is based on the **total requirement**, not a fixed number per car. \n\n \n

Step 6: Calculate total area needed for 200 cars.
\nSince the ground and basement must share the parking area equally, not the car count, the calculation is as follows: \n\nTotal area needed if all cars were in the ground floor = \(200 \times 15 = 3000\) m\(^2\).
\nTotal area needed if all cars were in the basement = \(200 \times 25 = 5000\) m\(^2\). \n\nHowever, given: The parking area is equally split between the two levels. \n\n\[\n\text{Total parking area required} = 200 \times \text{average area per car}\n\] \n\nWeighted average area per car = \(\frac{15+25}{2} = 20\) m\(^2\)/car.
\n\[\n\text{Total parking area} = 200 \times 20 = 4000 \; \text{m}^2\n\] \n\nTherefore, each level (ground + basement) receives: \n\[\n\frac{4000}{2} = 2000 \; \text{m}^2\n\] \n\n \n

Step 7: Calculate cars accommodated in the basement.
\n\[\n\text{No. of cars in basement} = \frac{2000}{25} = 80 \; \text{cars}\n\] \n\nRecheck: \n\nThe problem states that the **parking area is equally distributed between ground and basement**, not the number of cars. \n\n \n

Step 8: Perform the correct calculation.
\n- Total parking spaces required = 200.
\n- Each car requires 100 sq.m built-up ÷ FAR ÷ ratio → correction not needed. \n- Equal area distribution: 2000 m\(^2\) for basement ÷ 25 m\(^2\) per car = 80 cars. \n\n \n

Final Answer: \n\[\n\boxed{80 \; \text{cars}}\n\]