The weights of four boxes are 30 kg, 40 kg, 50 kg and 100 kg. Each box can be used at most once in a combination. Which of the following values cannot be the total weight, in kilograms, of any possible combination of these boxes?

Introduction / Context:

This is another combination and arithmetic reasoning question. We are given four fixed weights and asked to decide which of the given totals cannot be produced using any subset of these weights when each box is used at most once. Exam questions of this type train students to systematically consider all feasible combinations rather than guess.

Given Data / Assumptions:

• Box weights are 30 kg, 40 kg, 50 kg and 100 kg.
• Any box can appear in a combination either once or not at all.
• We may use one, two, three or all four boxes in making a total.
• We must find which option cannot be expressed as a valid sum.

Concept / Approach:

The best method is to compute or logically derive all distinct possible sums from the four given numbers. Because there are only four boxes, the total number of non-empty subsets is small. Once we list all possible totals, we simply compare them with the options and identify the one value that does not occur in our list.

Step-by-Step Solution:

Verification / Alternative check:

To be sure about 160 kg, try constructing it directly. Two-box combinations such as 100 + 50, 100 + 40, 100 + 30, 50 + 40 and 50 + 30 give totals of 150, 140, 130, 90 and 80 kilograms. Three-box combinations such as 100 + 40 + 30 or 100 + 50 + 30 give 170 and 180 kilograms. No combination yields exactly 160 kilograms, confirming that it is impossible.

Why Other Options Are Wrong:

Option 190 kg is obtainable as 40 + 50 + 100 = 190.

Option 180 kg is obtainable as 30 + 50 + 100 = 180.

Option 140 kg is obtainable as 40 + 100 = 140.

Common Pitfalls:

Students often forget one or more combinations or assume that if two nearby totals are possible then all intermediate values are also possible, which is not true when only specific weights are available. Careful listing or structured reasoning is essential for correctness in such discrete combination questions.

Final Answer:

The total weight that cannot be formed is 160 kilograms.