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

Step 1: List the fastest mode on each leg.
The trip has four legs travelled one after another, so the total travel time is just the sum of the time taken on each leg, whatever mode is picked on the other legs. That means we can work out the fastest and second fastest total by looking at each leg on its own.
Leg 1, Delhi to Bharatpur: bus, taxi and train all take 12 hours, so this leg is fixed at 12 hours regardless of mode.
Leg 2, Bharatpur to Jodhpur: train 12 hours, taxi 14 hours, bus 16 hours. Fastest is train at 12 hours.
Leg 3, Jodhpur to Jaipur: flight 2 hours, train 10 hours, bus 15 hours, taxi 15 hours. Fastest is flight at 2 hours.
Leg 4, Jaipur to Ajmer: train 4 hours, bus 5 hours, taxi 5 hours. Fastest is train at 4 hours.

Step 2: Work out the best (fastest) itinerary.
Add the fastest time on each leg: \( 12 + 12 + 2 + 4 = 30 \) hours. This is the smallest total travel time possible, using train for leg 2, flight for leg 3 and train for leg 4 (leg 1 can be any mode since all three tie at 12 hours).

Step 3: Find the smallest possible increase over the best itinerary.
To get the second best itinerary, swap out exactly one leg's fastest mode for its next fastest mode, whichever single swap adds the least extra time. Leg 1 cannot add any extra time since all three modes tie at 12 hours. On leg 2, moving from train (12 h) to taxi (14 h) adds 2 hours. On leg 3, moving from flight (2 h) to train (10 h) adds 8 hours. On leg 4, moving from train (4 h) to bus or taxi (5 h) adds only 1 hour, the smallest jump of the three legs.

Step 4: Build the second best itinerary and total.
Keep leg 2 on train and leg 3 on flight (both still at their fastest), and switch leg 4 from train to bus or taxi. The new total is \( 12 + 12 + 2 + 5 = 31 \) hours. Since 1 hour is the smallest possible increase available on any leg, no other single change gives a total between 30 and 31, so 31 hours is exactly the second best total travel time.

Final Answer:
The best itinerary takes 30 hours and the second best itinerary takes 31 hours. \[ \boxed{31 \text{ hours}} \]