The Mathematics of a Train Journey

Every journey teaches us something. My recent two-day trip to Hyderabad taught me mathematics, not the kind we learnt in school, but the kind that quietly plays with our assumptions. Every calculation I made seemed perfectly logical until reality stepped in to prove me wrong.

I had to travel to Hyderabad for a two-day function. I chose the train over a flight because the airfares for convenient timings were rather steep. After some research, I found what seemed to be the perfect combination, a Duronto Express for the onward journey and the Vande Bharat for the return.

A friend from Tamil Nadu, who was flying into Bengaluru that afternoon, was to join me on the Duronto. The train was scheduled to leave at 11.40 p.m. and arrive at Secunderabad at 8.35 a.m., a journey of 8 hours and 55 minutes.

After comparing all the available trains, I chose the Duronto. Except for the Vande Bharat, which completed the journey in just eight hours, every other train took over eleven hours. I happily concluded that I would be saving nearly three hours.

In any case, I reasoned, eight hours by train wasn't really much longer than flying. I would have to leave home at least three hours before departure, spend about an hour in the air, and then another hour and a half getting from the airport to my place of stay, including the inevitable wait for an Uber. The train suddenly seemed like the more sensible option.

Looking back, I realise I had been completely taken in by the "8 hours," almost ignoring the "55 minutes." Somehow, I had mentally rounded it down to just eight hours. Sometimes, numbers don't deceive us, we deceive ourselves by reading only the part we want to see!

The ticket, thanks to dynamic pricing, cost ₹1,840 and was waitlisted at numbers 47 and 48 when booked a week in advance.

My friend and I had kept driving to Hyderabad as a backup plan since both of us enjoy long drives. The difficulty was that the fate of the waitlisted tickets would be known only four hours before departure. My friend suggested that if the tickets remained uncertain by noon, I should simply drive to the airport, receive him on arrival, and we should head straight to Hyderabad. It was a sensible Plan B.

The previous day, the waitlist had moved only to 28 and 29. At that pace, confirmation appeared unlikely. Being the son of a railway employee, I thought I would try my luck with Tatkal booking. Logging into the IRCTC site proved harder than solving a mathematics problem. After several failed attempts from 10 a.m., I finally managed to log in around 1 p.m. and, to my delight, secured confirmed Tatkal tickets.

A quick calculation showed that the additional amount payable worked out to barely ₹221 per ticket after adjusting the cancellation and refund. I congratulated myself on having upgraded to confirmed tickets for such a small amount.

My happiness, however, was short-lived.

My sister, who also works in the Railways, reminded me that I had forgotten one important detail. My original waitlisted ticket itself had been booked at a dynamically inflated fare, about 34% higher than the normal fare. Suddenly, my brilliant arithmetic did not appear quite so brilliant!

Fortunately, I have developed the habit of finding solace in almost every situation. Instead of comparing the fare with the normal railway tariff, I compared it with the last-minute airfare for the same day. That immediately restored my happiness. Even after paying the premium railway fare, I was still saving well over ₹5,000 compared to flying.

Perspective, after all, often determines happiness more than mathematics.

Yeshwantpur station, meanwhile, seemed to be in a perpetual state of renovation. Accessing the platform, which was once straightforward, had become quite cumbersome. I had visited the station six months earlier and found the situation no better this time. With all the claims about the rapid transformation of Indian Railways, I wondered whether I was simply looking in the wrong places.

Once we settled into our berths, a pantry staff member came around after midnight asking passengers whether they preferred vegetarian or non-vegetarian breakfast. Half asleep, I quickly responded, "Vegetarian."

He smiled and replied, "I already know."

For a brief moment, I felt rather pleased, believing I belonged to a rare breed of passengers who had actually filled in their meal preference while creating the IRCTC profile.

That illusion too lasted only a few minutes.

A fellow passenger explained that the pantry staff was actually asking who wished to purchase breakfast. He also casually mentioned that if one unticked the meal option while booking, the ticket price would automatically reduce.

That immediately reminded me of my return journey by Vande Bharat. I recalled receiving SMS messages confirming tea, breakfast and lunch. Curious once again, I checked the meal charges. They came to around ₹360.

Another lesson learnt, sometimes what we pay for is not what we consciously choose.

After a reasonably comfortable night's sleep, we woke up, had tea and breakfast, and prepared to alight by 8.15 a.m. The train, however, rolled into Secunderabad only at 9.45 a.m.

Instead of the advertised 8 hours and 55 minutes, the journey had actually taken over ten hours. Interestingly, I had travelled by the same train in January and it had taken almost the same time then too.

I couldn't help wondering whether the advertised timing exists to make gullible travellers like me believe they are saving nearly three hours over other trains, only to discover later that the difference is barely an hour.

Secunderabad station too was under renovation. Looking at both Yeshwantpur and Secunderabad, I jokingly wondered whether the same contractor had been entrusted with both projects!

After two enjoyable days in Hyderabad, it was time to return by Vande Bharat.

We woke up at 4 a.m., had our coffee, got ready and reached Kacheguda station well before departure. My friend had another train to catch from SMVT Bengaluru at 4.45 p.m., so punctuality mattered.

Soon after departure came a series of announcements, repeated in English, Hindi, Telugu and Kannada.

Passengers were informed that:

- every passenger was entitled to a one-litre bottle of Rail Neer,

- toilets should be flushed after use, and

- smoking, including beedis, cigarettes and even agarbattis, was strictly prohibited because of smoke detectors.

Since I understood all four languages, these announcements seemed endless. More than the announcements themselves, what struck me was their content. Here was a premium train charging premium fares, repeatedly reminding passengers about the most basic civic responsibilities.

We often take pride in our rich culture, yet we still need loud public reminders to flush toilets and refrain from smoking inside trains. A simple notice near the toilets and a no-smoking sign might perhaps have conveyed the message just as effectively.

These announcements were repeated after almost every major halt.

Ironically, despite all the reminders, my friend returned from a walk through the train and reported that water from several toilets had overflowed into the passage.

Sometimes announcements alone cannot change behaviour.

The train remained around fifteen to twenty minutes behind schedule almost until Hindupur, the last stop before Bengaluru. My friend began worrying about his onward connection.

Then came the biggest surprise of the journey.

The Vande Bharat made up all the lost time and reached Yashwantpur Bengaluru at 1.30 p.m., a full thirty minutes ahead of its scheduled arrival. My friend comfortably caught the Metro and then an auto to reach SMVT station for his onward journey with time to spare.

As I reflected on the trip, I realised that almost every stage of the journey had challenged my assumptions. The advertised journey time, the dynamic pricing, the Tatkal arithmetic, the meal charges and finally the arrival time, each had taught me that numbers rarely tell the whole story.

Perhaps that is the real mathematics of travel. The calculations may begin with arithmetic, but they almost always end with perspective.

Stories, not instructions. Experiences, not advice—medical or otherwise. Data, only what the internet quietly gathers anyway. Proceed with equal parts curiosity and common sense.