Aptitude Discussion

Q. |
Dexter and Prexter are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1000 m. Dexter crosses 50 m 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 |

**Solution:**

Option(**B**) is correct

When Dexter completes the second round, they do handshake once.

Now for every round which Dexter completes, there will be one handshake as the ratio of speed is $13:8$.

$D$ and $P$ will meet at the pool end only after $D$ completes 26 rounds.

In the $20^{th}$ round, $D$ finish the race and the total handshake's will be:

$20−1 =\textbf{19}$

**Edit:** For an alternative solution, check comment by **Prasanna Jd.**

**Prasanna Jd**

*()
*

How about this?

Considering both of them start at the same time they have to do 20 times $(=\frac{1000}{50})$ to complete the race, now take Dexter as he is fast, in the first round they don't clap eachothre implies we are left with

$20-1=19$ chances

Since, both have started at same time.

When Dexter's 50m end Prexter lags by 1min,15sec. hence, this is the time period they meet each time in only 19 of the times.