In an autofair at Pragati Maidan, New Delhi, there are 600 vehicles consisting of only two wheelers and four whellers. A world renowned tyre agency visits the fair to survey the trye market which finds that there are total 2000 tyres are fixed in all the 600 vehicles, but without any stepney (or spare tyre). The number of two wheelers in the autofair is :

Options

A. 300
B. 400
C. 180
D. 200

Answer

To solve the problem, we need to find the number of two-wheelers in the auto fair, given that there are 600 vehicles in total and 2000 tyres fixed on these vehicles.

Let's break down the solution step by step:

### Step 1: Define 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 is 600:
\[ x + y = 600 \quad \text{(Equation 1)} \]
2. The total number of tyres is 2000. Since each two-wheeler has 2 tyres and each four-wheeler has 4 tyres, we can write:
\[ 2x + 4y = 2000 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing the entire equation by 2:
\[ x + 2y = 1000 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( x + y = 600 \) (Equation 1)
2. \( x + 2y = 1000 \) (Equation 3)

We can subtract Equation 1 from Equation 3 to eliminate \( x \):
\[ (x + 2y) - (x + y) = 1000 - 600 \]
This simplifies to:
\[ y = 400 \]

### Step 5: Substitute Back to Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 400 = 600 \]
Subtracting 400 from both sides gives:
\[ x = 200 \]

### Conclusion
The number of two-wheelers in the auto fair is \( \boxed{200} \).