Four boxes have weights 90 kg, 40 kg, 80 kg and 50 kg. Each box can be used at most once in a combination. Which of the following values cannot represent the total weight, in kilograms, of any possible combination of these four boxes?

Introduction / Context:

This quantitative aptitude question tests understanding of combinations and simple arithmetic. The aim is to decide which given total weight is not achievable when selecting some or all of the boxes exactly once. Such questions are common in banking and SSC exams because they check both logical completeness and careful calculation.

Given Data / Assumptions:

• There are four boxes with weights 90 kg, 40 kg, 80 kg and 50 kg.
• Any box can be used at most once in a combination.
• We can form totals using one, two, three or all four boxes.
• We need to identify which of the given totals cannot be obtained from any valid combination.

Concept / Approach:

The key idea is to list or logically derive all possible sums of these weights. Since there are only four boxes, the number of different non-empty subsets is limited. We systematically consider totals of one box, two boxes, three boxes and all four boxes. After that, we compare the list of achievable totals with the options and see which option does not appear in the list.

Step-by-Step Solution:

Verification / Alternative check:

We can also reason directly for 200 kg. The largest total less than or equal to 200 is 90 + 80 + 40 = 210, which is already more than 200. Any three-box total either equals 210, 180 or 170, none of which is 200. Testing all two-box combinations like 90 + 50, 90 + 40, 80 + 50 and 80 + 40 also shows that none equals 200. Therefore, 200 kg cannot be obtained by any allowed combination.

Why Other Options Are Wrong:

Option 260 kg is achievable by using all four boxes together: 90 + 40 + 80 + 50 = 260.

Option 180 kg is achievable via the three-box combination 90 + 40 + 50 = 180.

Option 170 kg is achievable via either 90 + 80 = 170 or 40 + 80 + 50 = 170.

Common Pitfalls:

Candidates often forget to include three-box combinations or accidentally reuse a box twice, which is not allowed. Another common mistake is to miss a valid combination or perform an incorrect addition, leading to a wrong conclusion about which total is impossible. Writing the combinations carefully and checking sums avoids these errors.

Final Answer:

The total weight that cannot be formed is 200 kilograms.