In a munciple parking thereare 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 can use the information provided about the total number of vehicles and the total number of wheels.

### Step 1: Define the variables
Let:
- \( x \) = number of two-wheelers
- \( y \) = number of four-wheelers

### Step 2: Set up the equations
From the problem, we know:
1. The total number of vehicles (two-wheelers + four-wheelers) is 175:
\[ x + y = 175 \quad \text{(Equation 1)} \]

2. The total number of wheels (two wheels per two-wheeler and four wheels per four-wheeler) is 520:
\[ 2x + 4y = 520 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:
\[ x + 2y = 260 \quad \text{(Equation 3)} \]

### Step 4: Solve the system of equations
Now we have two equations:
1. \( x + y = 175 \) (Equation 1)
2. \( x + 2y = 260 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (x + 2y) - (x + y) = 260 - 175 \]
This simplifies to:
\[ y = 85 \]

### Step 5: Substitute \( y \) back into Equation 1
Now we can substitute \( y = 85 \) back into Equation 1 to find \( x \):
\[ x + 85 = 175 \]
\[ x = 175 - 85 \]
\[ x = 90 \]

### Conclusion
The number of two-wheelers is \( \boxed{90} \).

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