It was impossibly arduous. Four days of problem solving, a break and another four more days of backbreaking labour that even future exceptional mathematicians found impossibly difficult. Most of the time the problems required a certain quickness in ability and the use of tricks to solve within the given time period. Mere aptitude in mathematics was not enough. It was and perhaps still is considered amongst the most difficult math exams in the world. (Some of us in the Indian system have a faint notion of the kind of problems that were set - what we called the S. L. Loney type - a sphere spinning on a needle that is balanced on an ellipsoid that is dangling from a pendulum or some such absurdity).
There was a certain caste system amongst those who succeeded. In the first class, the topper was the Senior Wrangler, followed by Second Wrangler, Third Wrangler and so on. The second class were the Senior Optimes followed by the Third Class, the Junior Optimes (yes, this is sounding more and more like Asterix). The last of the Junior Optimes was called a Wooden Spoon because tradition dictated that he (yes, always a he then) be given, by his friends a wooden spoon (actually a huge malting shovel lavishly decorated and inscribed in Greek) which the poor fellow was expected to take, hoist on his shoulder and carry it and himself out of the hall.
Senior Wranglers were God-like figures with all the attendant myth and mythology that would spring up around them. However they were not necessarily the best mathematicians, but, it was believed, would become the most influential one. After all, the Tripos stressed a certain knack in in solving problems fast rather than mathematical aptitude. Most future famous physicists and mathematicians were not Senior Wranglers (J. E. Littlewood was one notable exception). James Clerk Maxwell, J. J. Thomson, William Thomson (later Lord Kelvin) were all Second Wranglers. G. H. Hardy was, to his great consternation a Fourth Wrangler, Bertrand Russell a Seventh Wrangler.
Since the Tripos was impossible to 'max' without adequate practice, a whole alternate system of education cropped up around it. These were the coaching classes. Private coaches, for handsome fees, would coach you, not in the subtleties of mathematics but in how to take the Tripos. They would pour over old exams, make useful notes for solving problems, give you hours of practice all for the single minded purpose of taking the Tripos -- what someone called codifying mathematical knowledge into neat bundles. (Yes, yes, I know, it's familiar, but do bear with me, dear reader). The workload for students who took these mind numbing coaching classes was prodigious. For them, attending their usual lectures was a luxury they could ill afford. According to the famous mathematician J. E. Littlewood, himself a Senior Wrangler, one had to spend two thirds of the time practising solving difficult problems against time. Students frequently ignored the course material, in order to concentrate on the Tripos and hence the coaching classes. Hardy himself was coached by the legendary R. R. Webb, a 'producer' of many Senior Wranglers.
G. H. Hardy's aim was to eventually change this whole mind numbing examination system. His famous statement was that examinations (any examination, not just the Tripos) were necessary but only as an absolute minimum standard to get a degree. "An examination can do little harm as long as its standard is low", was his credo, instead of students and their tutors exhausting themselves to turn a comfortable second to a marginal first.
Hardy, despite his influence, succeeded in only marginally changing the system. On his pushing, a degree candidate still took the Tripos but was ranked only as Wrangler, Senior or Junior Optime, reducing somewhat the merciless pressure that the exam had created. The system had clearly more inertia than Hardy had bargained for, and he finally gave it to these minor changes.
The Indian analogy is obvious. The JEE is perhaps as stultifying, as mechanical as the Tripos (is or was). It stresses little knowledge of or ability in the subject, mainly a quickness of intellect and an ability to be able to use tricks to solve problems in the given time period. That is where coaching classes come in. It has today reached a stage where even the smartest students would not clear the JEE with a high rank without the knowledge of certain mathematical tricks in their kitty. Eventually all problems, even JEE problems can be solved without such tricks, but the race against time precludes a slow and methodical approach to any problem.
The Tripos system did produce some great scientists though few from amongst the toppers. Can the JEE boast of that? The numbers here are negligible and the names that spring to mind (for obvious reasons I don't wish to enter into a controversy about contemporary names who could be considered 'great') are hardly in the world class category of the Tripos toppers. More often than not, they end up in management, becoming CEOs or VPs of companies and only rarely a distinguished academic. The JEE is not a passport to greatness, not even as much as the admittedly flawed Tripos system. It's perhaps time for a significant change in the approach to this examination system -- though something tells me that that is not going to happen anytime soon. (It's also not in the interest of the coaching class companies to see it change). Like the British system which we inherited, the inertia in our system is large enough to neutralise even the most dedicated revolutionary.
Acknowledgement: As a product of the Indian and American education systems, I have little or no direct knowledge of the British Tripos system. Most of the stuff above is based on reading the literature, mainly the beautiful and fascinating account of the system in Robert Kanigel's masterful biography of Srinivasa Ramanujan.