Direction: A significant amount of traffic flows from point S to point T in the one-way street network shown below.
Points A, B, C and D are junctions in the network, and the arrows mark the direction of traffic flow.
The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.
Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum.
If two or more routes have the same least travel cost, then motorists are indifferent between them.
Hence, the traffic gets evenly distributed among all the least cost routes The government can control the flow of traffic only by levying appropriate toll at each junction.
For example, if a motorist takes the route S - A - T (using junction A alone), then the total cost of travel would be Rs 14 (i.e. Rs 9 + Rs 5) plus the toll charged at junction A.
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If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
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- 0, 5, 4, 1
- 0, 5, 2, 2
- 1, 5, 3, 3
- 1, 5, 3, 2
- 0, 4, 3, 2
Correct Option: A
According to question ,
If all the five routes have the same cost, then there will be an equal flow in all the five routes, i.e. 20% in each route.
But then the percentage of traffic in S - A = 20% (Only one route involving S - A)
S - B = 40% (As there are two routes involving S - B)
S - D = 40% (As there are two routes involving S - D)
But here the given condition that traffic in S-A is equal to that in S - B, which in turn is equal to S - D is not satisfied.
Of the routes, that can be used the number of routes involving S - A must be the same as S - B, which in turn is same as that as S - D.
That is possible only when we block the junction C and that can be done by taking higher toll charge at C to achieve this goal c > 3.
Hence , required answer will be option A .
