Q) Ram and Shyam are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1,000 m. Ram crosses 50 m in 2 min and Shyam in 3 min 15 s. Each time they meet/cross each other, they do handshake’s. How many such handshake’s will happen? (They both start from the same end at the same time.) options: a)18 b)19 c)23 d)20 e)17

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