In a parking lot there are only two types of vehicles: two-wheelers and four-wheelers. The total number of vehicles is 200, and the total number of wheels counted is 580. How many four-wheeler vehicles are there in the parking lot?

Introduction / Context:
This arithmetic reasoning question uses a simple system of linear equations to model a parking lot with two-wheelers and four-wheelers. You are given the total number of vehicles and the total number of wheels and must determine how many vehicles are four-wheelers. This type of problem frequently appears in aptitude tests to check understanding of simultaneous equations and logical setup.

Given Data / Assumptions:

• Total number of vehicles (two-wheelers plus four-wheelers) is 200.
• Each two-wheeler has 2 wheels.
• Each four-wheeler has 4 wheels.
• Total number of wheels is 580.
• There are no other types of vehicles besides two-wheelers and four-wheelers.

Concept / Approach:
Let the number of two-wheelers be T and the number of four-wheelers be F. The total vehicle count gives one equation, T + F = 200. The total wheel count gives another equation, 2T + 4F = 580. Solving this pair of linear equations will yield the values of T and F. Once F is known, we have the required number of four-wheelers.

Step-by-Step Solution:
Step 1: Let T be the number of two-wheelers and F be the number of four-wheelers. Step 2: From the total number of vehicles, T + F = 200. Step 3: From the total number of wheels, 2T + 4F = 580. Step 4: Simplify the wheels equation by dividing by 2: T + 2F = 290. Step 5: Now we have two equations: T + F = 200 and T + 2F = 290. Step 6: Subtract the first equation from the second: (T + 2F) - (T + F) = 290 - 200. Step 7: This gives F = 90. Step 8: Therefore, there are 90 four-wheelers in the parking lot.

Verification / Alternative check:
Using F = 90 in the first equation T + F = 200, we get T = 200 - 90 = 110 two-wheelers. Check the wheels: 110 two-wheelers contribute 110 * 2 = 220 wheels, and 90 four-wheelers contribute 90 * 4 = 360 wheels. Total wheels = 220 + 360 = 580, which matches the given data, confirming the solution is correct.

Why Other Options Are Wrong:
Option A 110 is actually the number of two-wheelers, not four-wheelers. Option C 100 and option D 180 do not satisfy both the vehicle count and the wheel count simultaneously when used in the equations, and so they are inconsistent with the given information.

Common Pitfalls:
A common error is to confuse the counts of two-wheelers and four-wheelers or to miswrite the wheel equation as 2T + 4F = 200 instead of equaling 580. Another pitfall is to try guessing values instead of solving the equations systematically, which can waste time and lead to mistakes. Writing and solving the equations clearly is the most reliable method.

Final Answer:
There are 90 four-wheelers in the parking lot.