How many rectangular meshes are there in 1 square metre of wire gauge if each mesh opening is 8 mm long and 5 mm wide?

Introduction / Context:
This aptitude problem checks understanding of area, unit conversion, and counting identical small regions inside a larger region. Such questions are common in topics like mensuration and practical mathematics, where students must convert between square metres and square millimetres and then use the idea of repeated patterns, here called meshes, to compute how many fit into a given area.

Given Data / Assumptions:
• Total area of the wire gauge sheet = 1 square metre.• Each mesh is a small rectangle of dimensions 8 mm by 5 mm.• All meshes are identical and arranged without gaps or overlaps.• We need the number of such meshes that exactly fit into 1 square metre.

Concept / Approach:
The number of small identical rectangles that can fit into a large rectangle is equal to the total area of the large rectangle divided by the area of one small rectangle, provided everything is neatly arranged. Here, the large area is given in square metres, while the mesh dimensions are in millimetres. Therefore, the key steps are to convert the large area into square millimetres, compute the area of one mesh in square millimetres, and then perform a simple division.

Step-by-Step Solution:
Step 1: Convert 1 square metre to square millimetres.1 metre = 1000 millimetres, so 1 square metre = 1000 mm * 1000 mm = 1000000 mm^2.Step 2: Compute the area of one mesh.Area of one mesh = length * width = 8 mm * 5 mm = 40 mm^2.Step 3: Compute the number of meshes.Number of meshes = total area / area of one mesh = 1000000 / 40.Step 4: Perform the division.1000000 / 40 = 25000 meshes.

Verification / Alternative check:
We can check the order of magnitude. If each mesh were roughly 10 mm by 10 mm (100 mm^2), we would expect about 1000000 / 100 = 10000 meshes in one square metre. Our mesh area is 40 mm^2, which is smaller, so more meshes should fit. 25000 is indeed larger than 10000, which is consistent with this rough estimate, confirming that the answer is reasonable.

Why Other Options Are Wrong:
Option A: 2500 is too small and would correspond to a much larger mesh area than 40 mm^2.Option C: 12500 represents half of the correct count and would result from using an incorrect area or conversion factor.Option D: 15400 is not supported by the exact area calculations and does not match any logical intermediate step.

Common Pitfalls:
Common mistakes include converting only line units but forgetting that area scales with the square of the conversion factor, for example treating 1 metre as 100 centimetres but then not squaring 100. Another error is to reverse the division and divide the small area by the large area, which gives a number less than one rather than a count of meshes. Careful handling of units and correct order of operations help avoid these errors.

Final Answer:
The number of meshes in 1 square metre of wire gauge is 25000.