The weights of four boxes are 70 kg, 50 kg, 30 kg and 90 kg. Which of the following cannot be obtained as the total weight, in kilograms, of any combination of these boxes if each box is used at most once?

Introduction / Context:
This arithmetic reasoning question tests your understanding of how to form different possible totals by combining a small set of distinct weights. You are given four box weights and asked to decide which one of the given totals cannot be formed when each box can be used at most once. Such questions are very common in reasoning and bank or SSC type competitive exams, and they quietly check both systematic counting and basic number sense.

Given Data / Assumptions:

• Available box weights: 70 kg, 50 kg, 30 kg, 90 kg.
• Each box can be used at most one time in a combination.
• We must check the totals: 220 kg, 240 kg, 210 kg, 170 kg.
• We assume there are no hidden conditions such as partial use of a box. Every used box contributes its full given weight.

Concept / Approach:
The key idea is to list or logically derive all distinct possible sums that can be formed by adding these four weights using each box at most once. For four numbers, there are combinations of one box, two boxes, three boxes, and all four boxes. Once we know these sums, we simply check which option is missing from this list. Working systematically avoids missing any combination or double counting a total.

Step-by-Step Solution:
Step 1: Write the weights: 70, 50, 30, 90.Step 2: Sums using one box: 30, 50, 70, 90.Step 3: Sums using two boxes: 30 + 50 = 80, 30 + 70 = 100, 30 + 90 = 120, 50 + 70 = 120, 50 + 90 = 140, 70 + 90 = 160.Step 4: Sums using three boxes: 30 + 50 + 70 = 150, 30 + 50 + 90 = 170, 30 + 70 + 90 = 190, 50 + 70 + 90 = 210.Step 5: Sum using all four boxes: 30 + 50 + 70 + 90 = 240.Step 6: Collect all distinct sums: 30, 50, 70, 80, 90, 100, 120, 140, 150, 160, 170, 190, 210, 240.Step 7: Compare the options: 220, 240, 210, 170 with this list of possible totals.

Verification / Alternative check:
A quick alternative check is to see whether 220 can be written as a sum of any subset of the four numbers. Try the largest combinations: 90 + 70 + 50 = 210, which is already less than 220 and adding 30 would overshoot to 240. Next, 90 + 70 + 30 = 190, and adding 50 gives 240. Other pairs: 90 + 50 = 140, 90 + 70 = 160, 90 + 30 = 120, 70 + 50 = 120, 70 + 30 = 100, 50 + 30 = 80. None of these give 220, confirming that 220 is not reachable.

Why Other Options Are Wrong:
240 kg is possible by using all four boxes: 30 + 50 + 70 + 90 = 240.210 kg is possible by using 50 kg, 70 kg and 90 kg: 50 + 70 + 90 = 210.170 kg is possible by using 30 kg, 50 kg and 90 kg: 30 + 50 + 90 = 170.The option that says None of these totals is incorrect because some of the given totals are indeed achievable.

Common Pitfalls:
Many learners try random additions and may miss a combination, leading them to wrongly believe that a valid sum is impossible or an impossible sum is valid. Another mistake is to assume that the question asks for the largest or smallest total, rather than the one that cannot be formed. Some students also misread the condition about using each box at most once and may accidentally reuse a weight, which completely changes the set of possible totals.

Final Answer:
The only total that cannot be formed from any combination of the given four box weights is 220 kilograms.