Question

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Q125. The second best option (in terms of travel time) gives a total travel time of ______ hours for the entire itinerary.

• A. 29
• B. 30
• C. 31
• D. 32

Hint:

Since the four legs are travelled one after another, total time is just the sum of each leg's chosen time. Find the fastest mode per leg for the best itinerary, then swap only the leg with the smallest possible time penalty to get the second best.

Answer 1

The Correct Option is C

This question is really about arithmetic, not probability. Since Ram travels Delhi to Bharatpur to Jodhpur to Jaipur to Ajmer in a straight sequence, the total trip time is simply the time of leg 1 plus leg 2 plus leg 3 plus leg 4, whatever modes are chosen.

First, list the travel time for every available mode on every leg:

• Delhi to Bharatpur: bus 12 h, taxi 12 h, train 12 h (all equal)
• Bharatpur to Jodhpur: train 12 h, taxi 14 h, bus 16 h
• Jodhpur to Jaipur: flight 2 h, train 10 h, bus 15 h, taxi 15 h
• Jaipur to Ajmer: train 4 h, bus 5 h, taxi 5 h

The lowest total comes from picking the lowest number in each leg: $12 + 12 + 2 + 4 = 30$ hours. That is the best (fastest) itinerary.

Now look for the second lowest total possible. Because the legs are independent, the next best total is just 30 plus the smallest "step up" available on any single leg, since only one leg needs to change to move to the next best combination:

• Leg 1 has no step up, every mode is 12 h.
• Leg 2's step up from train to taxi is $14 - 12 = 2$ h.
• Leg 3's step up from flight to train is $10 - 2 = 8$ h.
• Leg 4's step up from train to bus or taxi is $5 - 4 = 1$ h, the smallest of the three.

The smallest available step up is 1 hour, on leg 4. So the second best itinerary total is $30 + 1 = 31$ hours, reached by keeping leg 2 on train and leg 3 on flight, and switching leg 4 from train to bus or taxi.

Let's summarize:

• Best itinerary total time: 30 hours.
• Second best itinerary total time: 31 hours, since a 1 hour bump on the Jaipur to Ajmer leg is the cheapest possible change.

So the second best option gives a total travel time of 31 hours.