XAT 2012 — Decision Making Question 6
Answer the following questions on the basis of the information given in the following case.
Tina a blast furnace expert, who works as a technology trouble-shooter stays in Jamshedpur. She has got an important assignment in Delhi, which requires six hours to complete. The work is so critical that she has to start working the moment she reaches the client’s premises.
She is considering various options for her onward and return journey between Jamshedpur to Delhi.
A quick search revealed that ticket from Jamshedpur to Delhi is available in two trains. Trains 12801 and 12443 depart from Jamshedpur station at 06:45 hrs and 15.55 hrs and reach Delhi next day at 04:50 hrs and 10:35 hrs respectively. Trains 12444 and 12802 start from Delhi at 17:20 hrs and 22:20 hrs and reach Jamshedpur next day at 10:35 hrs and 20:05 hrs respectively.
Another option is to reach Ranchi by a three hour road trip and take a flight to Delhi from Ranchi. The distance between Ranchi and Delhi is covered in 105 minutes both-ways by any of the scheduled flights. Air India operates two flights, AI 9810 and AI 810, which depart Ranchi at 8:00 hrs and 15:25 hrs respectively. Flight number IT-3348 operated by Kingfisher Airlines departs Ranchi at 19:20 hrs. Return flights operated by Air India, AI 9809 and AI 809, depart Delhi at 5:50 hrs and 11:00 hrs respectively. Flight number IT-3347 operated by Kingfisher Airlines departs Delhi at 17:10 hrs.
From Tina’s home Jamshedpur railway station is five minutes drive, and her destination at Delhi is 90 minutes and 30 minutes drive from airport and railway station respectively. One has to reach the airport at least one hour before the scheduled departure to complete the boarding procedure. At every railway station she loses five minutes in navigating through the crowd.
If Tina wants to minimize the total time out of Jamshedpur, the best option for her, from the options given below, is:
Answer & solution
- A
AI 9810 and return by IT 3347.
AI 9810 and return by train number 12802.
- C
IT 3348 and return by AI 9809.
- D
Train number 12443 and return by train number 12444.
- E
AI 9810 and return by train number 12444.
Here, first calculate the time taken for each journey and tabulate it so as to help calculate the requisite values.
The timings from Jamshedpur to Delhi and from Delhi to Jamshedpur are as follows:
Also, the waiting time at the airport, navigation time at the railway station and work duration are:
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Now, keep in mind that each flight (in either direction) takes 105 minutes.
So, the time taken from Tina’s house to the work site will always remain constant. This will be:
Jamshedpur to Ranchi by car + Waiting time at airport + Flight time + airport to work site
= 180 + 60 + 105 + 90
= 435 minutes i.e. 7 hours and 15 minutes.
This will remain constant while returning from the work site to Jamshedpur as well.
Similarly, the time from Tina’s house to the Jamshedpur railway station (excluding train time) will be always be 10 minutes (5 for travel and 5 for navigation). This will remain constant even when she returns from Jamshedpur railway station to her house.
Also, the time from Delhi railway station to the work site will always be 35 minutes (30 for travel and 5 for navigation). Again, this will remain constant even when she returns from the work site to Delhi railway station.
Finally, work time will always be constant at 360 minutes
Also, always Total time = Travelling Time + Work Time + Waiting Time
Now, consider each option:
Option 1:
Since she travels by flight in both case, total travelling time = 435 × 2 = 870 minutes
Work time = 360 minutes
Now, if she goes by AI 9810, she reaches the site 90 minutes after 9:45 i.e. at 11:15 a.m. and finishes the work at 17:15. Because IT 3347 departs at 17:10 hours, she will have to wait till 14:40 hours on the next day i.e. wait time of 1285 minutes
So, total time = 870 + 360 + 1285 = 2515 minutes
Option 3:
Again, because she travels by flight both ways, travel time = 870 minutes
Work time = 360 minutes
Now, if she goes by IT 3348, she reaches the site 90 minutes after 21:05 i.e. at 22:35 hours and finishes the work at 04:35 hours. Because IT 3347 departs at 05:50 hours, she will have to wait till 03:20 hours on the next day i.e. wait time of 1365 minutes
So, total time = 870 + 360 + 1365 = 2595 minutes
Hence, option (c) can be eliminated.
Option 2:
She goes by flight and returns by train
Travel time = Flight time + Time from work site to Delhi railway station + Actual train travel + Time from Jamshedpur railway station to home = 435 + 35 + 1305 + 10 = 1785 minutes
Work Time = 360 minutes
Now, if she goes by AI 9810, she reaches the site 90 minutes after 9:45 i.e. at 11:15 a.m. and finishes the work at 17:15. Because train 12802 departs at 22:20 hours, she will have to wait till 21:45 hours on the same day i.e. wait time of 270 minutes
So, total time = 1785 + 360 + 270 = 2415 minutes
Hence, option (a) can be eliminated.
Option 5:
She goes by flight and returns by train
Travel time = Flight time + Time from work site to Delhi railway station + Actual train travel + Time from Jamshedpur railway station to home = 435 + 35 + 1035 + 10 = 1515 minutes
Work Time = 360 minutes
Now, if she goes by AI 9810, she reaches the site 90 minutes after 9:45 i.e. at 11:15 a.m. and finishes the work at 17:15. Because train 12444 departs at 17:20 hours, she will have to wait till 16:45 hours on the next day i.e. wait time of 1410 minutes
So, total time = 1515 + 360 + 1410 = 3285 minutes
Hence, option (e) can be eliminated.
Option 4:
She travels both ways by train
So, the journey between her house and Jamshedpur railway station will be counted twice and the journey between the workplace and Delhi railway station will be counted twice. Also, the actual train time will be counted once each for the two journeys.
Travel Time = (10 × 2) + (35 × 2) + 1120 + 1035 = 2245 minutes
Work time = 360 minutes.
Now, observe that work time and travel time together are 2245 + 360 = 2605 minutes which is greater than the least time obtained for option 2. So, there is no point in calculating the waiting time which will only increase this value.
Hence, option (d) can be eliminated.
Hence, option (b).