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  • A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with The flight durati

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with The flight duration between any pair of cities will be less than one hour To start operations, the company has to decide on a daily schedule.


The underlying principle that they are working on is the following:


Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day

Question :  Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A. B and C. Further, suppose that direct flights are allowed Only between two cities satisfying one of the following:

1, Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4 Between C and any city in G4

Then the minimum number of direct flights that satisfies the underlying principle of the airline is

 

Option: 1

40


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

The underlying principle of the airline is that any person staying in any of the 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day. This means that there must be at least one morning flight and one evening flight between any pair of cities that are allowed to have direct flights.

The 10 cities are divided into 4 groups, G1, G2, G3, and G4, with 3, 3, 2, and 2 cities in each group, respectively. Group G1 consists of cities A, B, and C.

The direct flights that are allowed are:

Between two cities in G1.

Between A and any city in G2.

Between B and any city in G3.

Between C and any city in G4.

The minimum number of direct flights that must be scheduled to satisfy the underlying principle is:

Between the cities of G1: \mathrm{3C2\times4=12~flights.}

Between A and any city in G2: \mathrm{3\times4=12~flights.}

Between B and any city in G3: \mathrm{2\times4=8~flights.}

Between C and any city in G4: \mathrm{2\times4=8~flights.}

Total: 12 + 12 + 8 + 8 = 40 flights.

Therefore, the minimum number of direct flights that must be scheduled is 40.

Posted by

vinayak

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