# CAT 2006 Question Paper

Instructions

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 traveling from point S to point T would obviously take the route for which the total cost of traveling 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.

Question 41

Question 42

Question 43

Question 44

Question 45

## The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

Instructions

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

1.  A team must include exactly one among P,R and S.
2.  A team must include either M or Q, but not both.
3.  If a team includes K, then it must also include L, and vice versa.
4.  If a team includes one among S, U and W, then it should also include the other two.
5.  L and N cannot be members of the same team.
6.  L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.

Question 46

Question 47

Question 48

Question 49

Question 50