There are six companies, 1 through 6. All of these companies use six operations, A through F. The following graph shows the distribution of efforts put in by each company in these six operations
Question: 1
Suppose effort allocation is inter-changed between operations B and C, then C and D, and then D and E. If companies are then ranked in ascending order of effort in E, what will be the rank of company 3?
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When swapping sequentially, track each operation’s value step-by-step to avoid errors.
Original effort for company 3 in E = 21.8%. After swaps:
- Swap B and C: B (16.4) ↔ C (10.9) → E unchanged.
- Swap C and D: New C = 16.3, D = 10.9.
- Swap D and E: New E = 16.3 (old D).
Ranking E across companies after swaps puts company 3 in 4th place.
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Question: 2
A new technology is introduced in company 4 such that the total effort for operations B through F get evenly distributed among these. What is the change in the percentage of effort in operation E?
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When redistributing evenly, divide the total among the new number of categories and compare with original values.
For company 4: Sum of B–F = 10.3 + 8.2 + 11.2 + 28.6 + 23.4 = 81.7. Equal distribution among 5 operations = 81.7 / 5 ≈ 16.34% each. Original E = 28.6%. Change = 16.34 – 28.6 ≈ -12.3%.
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Question: 3
Suppose the companies find that they can remove operations B, C and D and redistribute the effort released equally among the remaining operations. Then which operation will show the maximum across all companies and all operations?
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Apply redistribution company-wise and then scan for the global maximum after adjustments.
Removing B, C, D redistributes their total equally to A, E, F in each company. For company 4: B+C+D = 10.3 + 8.2 + 11.2 = 29.7. Each of A, E, F gains 29.7 / 3 = 9.9. New E = 28.6 + 9.9 = 38.5, the highest among all adjusted values.