Given below is a network of oil pipelines and nine hubs– A through I. The requirement of oil at the hubs is exactly met by the flow in the pipelines. The flow in some of the pipelines and the requirement at some of the hubs is also mentioned. A is the only hub which is a source hub, i.e. the hub A does not have any requirement of its own but it supplies the requirement of all the other hubs.
It is also known that
I. The maximum capacity of any pipeline is 1000.
II. The requirement at any hub except A and I is equal to the flow in exactly one of the pipelines directly connected to it.
III. No two pipelines directly connected to the same hub carry the same amount of oil.
IV. The flow in none of the pipelines shown above is zero.
What is the amount of oil carried by the pipeline D-G?
From the 1st statement: B2 is now as old as B3 was in the past. Hence B2 is younger to B3 or B2 < B3. Also sometime in the past B1 was twice as old as B4. So B1 is elder to B4 or B1 > B4. B3 will be as old as B5 in future, hence B3 < B5. The second statement suggests: B1 > B6. B1 was as old as B7 in the past. Hence B1 > B7. B4 will be as old as B6 in future. Hence B6 > B4. B6 will be as old as B7 now in future. Hence B7 > B6. B7 was as old as B2, when B1 was as old as B7. Hence B1 = B2. Combining both the results, we get: and B5 > B3 > B2 = B1 > B7 > B6 > B4 (Note by B1 = B2, it is meant that they are of similar age group, not necessarily the same).
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