Two swimmers, Ankit and Bipul, start swimming from opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is-

Consider the speeds of Ankit and Bipul as $$A$$ and $$B$$ respectively. The total distance of the swimming pool is covered by Ankit in 10 minutes and by Bipul in 15 minutes. This gives us the following relation:

$$10A=15B$$  or  $$A:B=3:2$$. We can therefore assume the value of $$A$$ as $$3k$$ and the value of $$B$$ as $$2k$$. This makes the total length of the swimming pool $$3k*10 = 2k*15 = 30k$$

Since they are running in the same direction, the first meeting will be at $$\dfrac{30k}{3k+2k} = 6$$ minutes. $$80-6=74$$ minutes of their journey is still remaining.

Since they are swimming back and forth, the entire back and forth journey can be taken as a circular track the length of which is double the length of the swimming pool, or $$30k+30k=60k$$. 

On this circular journey, Ankit and Bipul will meet every $$\dfrac{60k}{3k+2k}=12$$ minutes. In remaining $$74$$ minutes of journey, therefore, they will meet a total of $$\lfloor \frac{74}{12} \rfloor = 6$$ times. 

Along with the first meeting after $$6$$ minutes, there will thus be a total of $$6+1=7$$ meetings in total in a span of $$80$$ minutes.