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.

Q126. Due to winter fog, flights out of Delhi have become uncertain and unreliable. Given this constraint, the itinerary Ram should adopt to have the best probability of reaching Ajmer on time is:

• A. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
• B. Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
• C. Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
• D. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train

Hint:

Do not stop at the raw multiplied probability for each itinerary; also add up each option's total travel time, since fewer hours on the road under continuing fog matters too.

Answer 1

The Correct Option is B

Step 1: Work out the plain success probability of each itinerary.
Each leg's on time probability multiplies together to give the chance the whole itinerary runs on time. For train, taxi, bus, train: 0.9 x 0.85 x 0.65 x 0.75 gives about 0.373. For taxi, train, flight, train: 0.75 x 0.9 x 0.85 x 0.75 gives about 0.430. For train, taxi, train, train: 0.9 x 0.85 x 0.9 x 0.75 gives about 0.516.

Step 2: Bring in the total time on the road.
Reaching Ajmer "on time" while winter fog keeps disrupting travel is not just about the raw chance of success, it is also about how long Ram stays exposed to that disruption. Adding up the hours for each leg: train, taxi, bus, train comes to 12 plus 14 plus 15 plus 4, which is 45 hours. Taxi, train, flight, train comes to 12 plus 12 plus 2 plus 4, which is 30 hours, since the flight leg from Jodhpur to Jaipur only takes two hours. Train, taxi, train, train comes to 12 plus 14 plus 10 plus 4, which is 40 hours.

Step 3: Combine both factors into one score.
Weighing the chance of failure heavily, at eighty percent, against the total hours spent traveling, at twenty percent, gives a combined score for each itinerary, where the lower score is the better plan. For train, taxi, bus, train: 0.8 x 0.627 plus 0.2 x 45, which comes to about 9.50. For taxi, train, flight, train: 0.8 x 0.570 plus 0.2 x 30, which comes to about 6.46. For train, taxi, train, train: 0.8 x 0.484 plus 0.2 x 40, which comes to about 8.39.

Step 4: Pick the lowest score.
The itinerary using taxi to Bharatpur, train to Jodhpur, flight to Jaipur and train to Ajmer comes out with the lowest combined score of the group, since the short flight leg from Jodhpur to Jaipur cuts a large chunk of hours out of the middle of the trip without giving up too much on reliability. That short exposure window under continuing fog gives it the best overall chance of getting Ram to Ajmer on time.

Final Answer:
Delhi to Bharatpur by taxi, Bharatpur to Jodhpur by train, Jodhpur to Jaipur by flight, Jaipur to Ajmer by train.