Arithmetic

Time, Speed & Distance

Hard

Two swimmers, Ankit and Bipul, start swimming from the 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

✅ Correct Option: 3

Given:

Ankit covers the pool in 10 minutes
Bipul covers the pool in 15 minutes
They swim back and forth for 80 minutes
They start from the same end going in opposite directions

Find Their Speeds:

Let the pool length be $L$ .

Ankit's speed: $A = \frac{L}{10}$

Bipul's speed: $B = \frac{L}{15}$

From $10A = 15B$ , we get the speed ratio:

$A : B = 3 : 2$

Let $A = 3k$ and $B = 2k$ (where $k$ is a constant)

Then the pool length: $L = 10 \times 3k = 30k$

First Meeting:

Since they start from the same point going in opposite directions, they approach each other.

Combined approach speed = $A + B = 3k + 2k = 5k$

Time to first meeting:

$t_1 = \frac{L}{A + B} = \frac{30k}{5k} = 6 \text{ minutes}$

Remaining time: $80 - 6 = 74$ minutes

Pattern of Subsequent Meetings:

After the first meeting, they continue swimming back and forth. We can model this as a circular track of length $2L = 60k$ (one complete lap = down and back).

On this circular path, they meet repeatedly at regular intervals.

Time between consecutive meetings:

$\Delta t = \frac{2L}{A + B} = \frac{60k}{5k} = 12 \text{ minutes}$

Count Total Meetings:

Meetings in the remaining 74 minutes:

$\left\lfloor \frac{74}{12} \right\rfloor = \left\lfloor 6.167 \right\rfloor = 6 \text{ meetings}$

Total meetings:

$\text{First meeting} + \text{Subsequent meetings} = 1 + 6 = 7$

Meeting Timeline:

Meeting #	Time (minutes)
1st	6
2nd	18
3rd	30
4th	42
5th	54
6th	66
7th	78

Answer: They meet 7 times in 80 minutes

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Solution

Meeting Timeline:

Answer: They meet 7 times in 80 minutes

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