Question: If Tina wants to minimize the total time out of Jamshedpur, the best option for her, from the options given below, is:
Explanation:
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:
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).