The weights of 4 boxes are 90, 30, 40 and 60 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes and in a combination a box can be used only once?

Options

A. 200
B. 220
C. 180
D. 130

Explanation

To solve the problem, we need to determine which total weight cannot be achieved by any combination of the given box weights: 90 kg, 30 kg, 40 kg, and 60 kg.

### Step-by-Step Solution:

1. **List the weights of the boxes:**
- The weights of the boxes are:
- Box 1: 90 kg
- Box 2: 30 kg
- Box 3: 40 kg
- Box 4: 60 kg

2. **Calculate the total weight of all boxes:**
- Total weight = 90 + 30 + 40 + 60
- Total weight = 220 kg

3. **Identify possible combinations:**
- We can use combinations of these weights to find different total weights. We will consider the following combinations:
- Using no boxes: 0 kg
- Using Box 1: 90 kg
- Using Box 2: 30 kg
- Using Box 3: 40 kg
- Using Box 4: 60 kg
- Using Box 1 and Box 2: 90 + 30 = 120 kg
- Using Box 1 and Box 3: 90 + 40 = 130 kg
- Using Box 1 and Box 4: 90 + 60 = 150 kg
- Using Box 2 and Box 3: 30 + 40 = 70 kg
- Using Box 2 and Box 4: 30 + 60 = 90 kg
- Using Box 3 and Box 4: 40 + 60 = 100 kg
- Using Box 1, Box 2, and Box 3: 90 + 30 + 40 = 160 kg
- Using Box 1, Box 2, and Box 4: 90 + 30 + 60 = 180 kg
- Using Box 1, Box 3, and Box 4: 90 + 40 + 60 = 190 kg
- Using Box 2, Box 3, and Box 4: 30 + 40 + 60 = 130 kg
- Using all boxes: 90 + 30 + 40 + 60 = 220 kg

4. **List all possible weights:**
- The possible weights we can achieve are:
- 0 kg, 30 kg, 40 kg, 60 kg, 70 kg, 90 kg, 100 kg, 120 kg, 130 kg, 150 kg, 160 kg, 180 kg, 190 kg, 220 kg

5. **Identify which weight cannot be achieved:**
- Now, we check the options provided (not mentioned in the question, but let's assume they are 200 kg, 210 kg, etc.).
- From our list, we see that 200 kg is not present. Therefore, 200 kg cannot be achieved with any combination of the boxes.

### Conclusion:
The total weight that cannot be achieved by any combination of the boxes is **200 kg**.