In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/ motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is

The correct option is 50.

Let us break down the problem step-by-step to understand the logical derivation. Let:
- C be the number of parked cars (four-wheelers).
- S be the number of parked scooters or motorbikes (two-wheelers).

From the above definitions, the total number of parked vehicles, which we will call V, is given by the sum of the cars and scooters:

$$V=C+S$$

Each car has 4 wheels, and each scooter has 2 wheels. Therefore, the total number of wheels, which we will call W, is given by:

$$W=4C+2S$$

According to the given condition, the total number of wheels is 100 more than twice the total number of parked vehicles. We can express this relationship mathematically as:

$$W=2V+100$$

Substitute the expressions for V and W into this equation:

$$4C+2S=2(C+S)+100$$

Now, expand the right side of the equation:

$$4C+2S=2C+2S+100$$

To solve for C, we can simplify the equation. Notice that the term 2S appears on both sides. Subtracting 2S from both sides gives:

$$4C=2C+100$$

Subtract 2C from both sides to group the C terms together:

$$2C=100$$

Divide both sides of the equation by 2 to find the number of cars:

$$C=50$$

Thus, the number of cars parked in the area is 50.