In a municipal parking there are some two wheelers and rest are 4 wheelers. If wheels are counted, there are total 520 wheels but the incharge of the parking told me that there are only 175 vehicles. If no vehicle has a stepney, then the no. of two wheelers is :

Options

A. 75
B. 100
C. 90
D. 85

Answer

To solve the problem step by step, we will define variables and set up equations based on the information provided.

### Step 1: Define Variables
Let:
- \( T \) = number of two-wheelers
- \( F \) = number of four-wheelers

### Step 2: Set Up the First Equation
According to the problem, the total number of vehicles is 175. Therefore, we can write the first equation as:
\[ T + F = 175 \]

### Step 3: Set Up the Second Equation
Next, we know that two-wheelers have 2 wheels each and four-wheelers have 4 wheels each. The total number of wheels counted is 520. Thus, we can write the second equation as:
\[ 2T + 4F = 520 \]

### Step 4: Simplify the Second Equation
We can simplify the second equation by dividing all terms by 2:
\[ T + 2F = 260 \]

### Step 5: Set Up the System of Equations
Now we have a system of two equations:
1. \( T + F = 175 \) (Equation 1)
2. \( T + 2F = 260 \) (Equation 2)

### Step 6: Solve the System of Equations
We can subtract Equation 1 from Equation 2 to eliminate \( T \):
\[ (T + 2F) - (T + F) = 260 - 175 \]
This simplifies to:
\[ F = 85 \]

### Step 7: Substitute to Find \( T \)
Now that we have \( F \), we can substitute it back into Equation 1 to find \( T \):
\[ T + 85 = 175 \]
Subtracting 85 from both sides gives:
\[ T = 175 - 85 \]
\[ T = 90 \]

### Conclusion
The number of two-wheelers is \( T = 90 \).

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