Question: A school in Chennai is planning for an excursion tour for its students. They want to show them KANYAKUMARI, VIZAG, and BHUBANESWAR, not necessarily in the same order. What is the minimum travel cost (in RS.) the school should charge from each of the student for the entire tour?
Explanation:
Observe that on a per-km basis, ship is the cheapest and airplane is the costliest. Hence, between the given cities, try to select the order of travel such that most of the journey is done by ship, followed by bus, then train and so on.
The overall route to be followed is: Chennai – city 1 – city 2 - city 3 - Chennai.
Chennai is connected to Kanyakumari and Vizag by train and to Bhubaneshwar by ship.
Among the three given cities, Kanyakumari is also the farthest from Chennai.
Hence, Chennai to Kanyakumari is always costlier than Chennai to the other two cities.
Hence, those two cities should be the first and last to be visited (in any order, due to the symmetry of the journey) while Kanyakumari should be visited between the two, as shown below.
Chennai → Vizag/Bhubaneshwar → Kanyakumari → Bhubaneshwar/ Vizag → Chennai
Now, find individual costs:
Chennai – Vizag: (300 × 2.5) = 750
Chennai – Bhubaneshwar: (950 × 1.5) = 1425
Vizag – Kanyakumari: (250 ×1.5) = 375
Kanyakumari – Bhubaneshwar: (700 ×2.5) = 1750
The total cost is Rs. 4300/-.
Hence, option (a).