1) There are quite a few formulae and concepts in Number System. Knowing the concepts beforehand will help you to get to the trick immediately after reading the question. This saves a lot of time which can be used better elsewhere.
2) A lot of practice is required. Practice all types of problems, but concentrate more on remainders, HCF-LCM and base system as questions from these topics can be quite tricky.
3) Don't depend a lot on the given calculator as it takes a lot of time in clicking each button. Improving your calculation speed will significantly help to reduce the amount of time you spend on a question.
When the faster swimmer meets (overtakes) the slower swimmer for the first time, the faster swimmer would have covered 2 laps (one lap = 50m) more than the slower swimmer, and both are swimming in the same direction at this point of time. Let this time be t.
So, t/2 = t/3.25 + 2 => t = 10.4 minutes
So, the faster swimmer overtakes the slower swimmer for the first time at 10.4 minutes after the start of the race. Number of handshakes till then = 5 (they cross each other 4 times and meet one time)
So, number of handshakes by t = 31.2 minutes = 15
From this moment, the 5th handshake occurs at t = 41.6 minutes. But the faster swimmer would have stopped swimming by then.
So, number of handshakes from t = 31.2 to t = 40 is 4
Total number of handshakes = 19
A ran 1000 m in the time that C ran 400 m. So, ratio of speeds of A and C is 5:2
Let the ratio of speeds of A, B and C be 5:x:2. So, speeds = 5k, xk and 2k
Time taken by B - Time taken by A = 1000/xk - 1000/5k = 60 seconds
Time taken by C - Time taken by B = 1000/2k - 1000/xk = 30 seconds
Equating for k, we get, 200*(5/x - 1)/60 = 500*(1-2/x)/30 => x = 2.5
So, speed of A : Speed of B = 5 : 2.5 = 2:1