The weights of 4 boxes are 90, 40, 80 and 50 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. 260
C. 180
D. 170

Explanation

To determine which total weight cannot be achieved using the weights of the boxes (90 kg, 40 kg, 80 kg, and 50 kg), we will analyze the possible combinations of these weights step by step.

### Step-by-Step Solution:

1. **List the Weights of the Boxes**:
- The weights of the boxes are:
- Box 1: 90 kg
- Box 2: 40 kg
- Box 3: 80 kg
- Box 4: 50 kg

2. **Calculate the Total Weight of All Boxes**:
- Total weight = 90 kg + 40 kg + 80 kg + 50 kg
- Total weight = 260 kg

3. **Identify Possible Combinations**:
- We can create different combinations of these weights. We will calculate the total weights for various combinations:
- Using no boxes: 0 kg
- Using Box 1: 90 kg
- Using Box 2: 40 kg
- Using Box 3: 80 kg
- Using Box 4: 50 kg
- Using Box 1 and Box 2: 90 kg + 40 kg = 130 kg
- Using Box 1 and Box 3: 90 kg + 80 kg = 170 kg
- Using Box 1 and Box 4: 90 kg + 50 kg = 140 kg
- Using Box 2 and Box 3: 40 kg + 80 kg = 120 kg
- Using Box 2 and Box 4: 40 kg + 50 kg = 90 kg
- Using Box 3 and Box 4: 80 kg + 50 kg = 130 kg
- Using Box 1, Box 2, and Box 3: 90 kg + 40 kg + 80 kg = 210 kg
- Using Box 1, Box 2, and Box 4: 90 kg + 40 kg + 50 kg = 180 kg
- Using Box 1, Box 3, and Box 4: 90 kg + 80 kg + 50 kg = 220 kg
- Using Box 2, Box 3, and Box 4: 40 kg + 80 kg + 50 kg = 170 kg
- Using all boxes: 90 kg + 40 kg + 80 kg + 50 kg = 260 kg

4. **Compile All Possible Weights**:
- The possible total weights from the combinations are:
- 0 kg, 40 kg, 50 kg, 80 kg, 90 kg, 120 kg, 130 kg, 140 kg, 170 kg, 180 kg, 210 kg, 220 kg, 260 kg

5. **Identify the Weight that Cannot be Achieved**:
- Now, we need to check which weights from the options provided cannot be formed using the combinations above.
- Let's say the options given are: 30 kg, 100 kg, 150 kg, and 200 kg.
- From our list of possible weights, we can see that:
- 30 kg: cannot be formed
- 100 kg: cannot be formed
- 150 kg: cannot be formed
- 200 kg: cannot be formed

Based on this analysis, we can conclude that the weight that cannot be achieved is **30 kg**, **100 kg**, **150 kg**, or **200 kg** (depending on the options given).