A box contains 90 screws each weighing 100 g and 100 bolts each weighing 150 g. If the total weight of the box together with all the screws and bolts is 35.5 kg, what is the weight of the empty box alone?

Introduction:
This problem tests your understanding of unit conversion between grams and kilograms and your ability to separate the weight of contents from the weight of a container. It is a typical aptitude question on arithmetic and averages in the context of weights and measures.

Given Data / Assumptions:

• Number of screws = 90, each of weight 100 g.
• Number of bolts = 100, each of weight 150 g.
• Total weight of box plus all contents = 35.5 kg.
• We assume 1000 g = 1 kg.
• The weight of the box is constant and does not vary with the contents.

Concept / Approach:
We first compute the total weight of screws and bolts in kilograms. Then we subtract that total contents weight from the combined weight (box plus contents) to find the weight of the empty box. This is a straightforward application of addition, multiplication, and subtraction with unit conversion.

Step-by-Step Solution:
Step 1: Total weight of screws = 90 * 100 g = 9000 g. Step 2: Total weight of bolts = 100 * 150 g = 15000 g. Step 3: Total weight of all items in grams = 9000 g + 15000 g = 24000 g. Step 4: Convert 24000 g to kg: 24000 / 1000 = 24 kg. Step 5: Total given weight (box + items) = 35.5 kg. Step 6: Weight of empty box = 35.5 kg - 24 kg = 11.5 kg.

Verification / Alternative check:
If the box alone weighs 11.5 kg, then box plus items should weigh 11.5 kg + 24 kg = 35.5 kg, which matches the given total. This confirms that our calculation is consistent and correct.

Why Other Options Are Wrong:

• 10.5 kgs: Gives total weight 10.5 + 24 = 34.5 kg, not 35.5 kg.
• 12 kgs: Gives total weight 12 + 24 = 36 kg, which is too high.
• 9.6 kgs: Gives total weight 9.6 + 24 = 33.6 kg, which is too low.
• 8.5 kgs: Also does not match the required total when added to 24 kg.

Common Pitfalls:
A common mistake is forgetting to convert grams into kilograms or mixing up 150 g as 0.15 kg instead of 0.150 kg. Others may incorrectly add the numbers or subtract in the wrong direction. Always keep units consistent and carefully distinguish between box weight and contents weight.

Final Answer:
The weight of the empty box is 11.5 kgs.