The average weight of all the vehicles in a parking is 4000 kg. The average weight of 12 vehicles is 6000 kg. Average weight of the remaining vehicles is 3000 kg. Whatis the total numberof vehicles in the parking?

Options

A. 40
B. 36
C. 20
D. 30

Answer

To find the total number of vehicles in the parking, we can follow these steps:

### Step 1: Understand the given data
- The average weight of all vehicles in the parking = 4000 kg.
- The average weight of 12 vehicles = 6000 kg.
- The average weight of the remaining vehicles = 3000 kg.

### Step 2: Set up the equation for total weight
Let the total number of vehicles in the parking be \( N \).

The total weight of all vehicles can be calculated using the average weight:
\[ \text{Total weight of all vehicles} = \text{Average weight} \times \text{Total number of vehicles} = 4000 \times N \]

### Step 3: Calculate the total weight of the 12 vehicles
The total weight of the 12 vehicles is:
\[ \text{Total weight of 12 vehicles} = \text{Average weight} \times \text{Number of vehicles} = 6000 \times 12 = 72000 \text{ kg} \]

### Step 4: Set up the equation for the remaining vehicles
Let the number of remaining vehicles be \( N - 12 \). The total weight of these remaining vehicles is:
\[ \text{Total weight of remaining vehicles} = \text{Average weight} \times \text{Number of remaining vehicles} = 3000 \times (N - 12) \]

### Step 5: Write the equation for total weight
Now, we can write the equation for the total weight:
\[ 4000N = 72000 + 3000(N - 12) \]

### Step 6: Simplify the equation
Expanding the right side:
\[ 4000N = 72000 + 3000N - 36000 \]
\[ 4000N = 3000N + 36000 \]

### Step 7: Solve for \( N \)
Now, subtract \( 3000N \) from both sides:
\[ 4000N - 3000N = 36000 \]
\[ 1000N = 36000 \]
\[ N = \frac{36000}{1000} = 36 \]

### Step 8: Conclusion
The total number of vehicles in the parking is \( N = 36 \).