Logical Reasoning Discussion

**Common Information**

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.

Q. |
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: |

✔ A. |
0, 5, 4, 1 |

✖ B. |
0, 5, 2, 2 |

✖ C. |
1, 5, 3, 3 |

✖ D. |
1, 5, 3, 2 |

✖ E. |
0, 4, 3, 2 |

**Solution:**

Option(**A**) is correct

If we make the cost of travelling on all the routes equal, traffic along S-B will be twice that along S-A.

But we want traffic along S-A, S-B and S-D to be the same.

As routes lead to C from both B and D, we can increase the toll at C so that the cost of travelling along S-B-C-T and S-D-C-T is more than that along the other three routes.

Now, 14 + *a* = 9 + *b* = 13 + *d*

∴ *a* = 0, *b* = 5 and *d* =1

Also, 7 + *b* + *c* > 14 and 10 + *d* + *c* > 14

∴ *c* > 3

Hence, **option A** is the correct choice.