Dexter and Prexter are competing with each other in a friendly community competition in a pool of 50m length and the race is for 1000m. Dexter crosses 50m in 2 min and Prexter in 3 min 15 sec. Each time they meet/cross each other, they do handshake's. How many such handshake's will happen if they start from the same end at the same time? A.18 B.19 C.20 D.17
how to approach these types of questions ? please explain with well solution. here is the reference link - see Question 36.
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Total race = 1000m
Length of pool = 50m
To complete 1000m one has to complete 20 rounds of 50 each.
They will meet at the same side only at 26th round as 2 & 3.25 LCM is 26 but we know race ends after 20 rounds.
So they will meet at each round except the first as they are starting from the same side and Dexter will take an early lead.
20-1 = 19
Firs off: notice the race lasts 40 minutes.
Note Dexter and Prexter are only simultaneously at the edge of the pool at minute 26. Since Dexter is at the edge after an even amount of minutes and Prexter is at the edge after a multiple of $3.25$ minutes, the only even multiple of $3.25$ under $40$ is $26$. So they are only at the edge at the same time at minute 26. However they are at opposite edges, since $2*13=26=3.25*8$ and $13$ is odd while $8$ is even. Thus the number of handshakes in an edge is 0.
Since the only time both Dexter and Prexter cross the lap at the same time is at the start this means each time Dexter crosses the pool after the first time he will cross Prexter and shake his hand, Dexter does this 19, thus the answer is 19.