Arti and Barkha start swimming towards each other from the deep end and shallow end respectively of a swimming pool in Funcity. They start their swimming simultaneously in the length of 300 m pool. The ratio of their speeds is 1:2 respectively. Each swimmer rests for 6 seconds once she reaches the other end starts swimming back. Where will they meet for the second time in the still water of swimming pool?

Options

A. 30 m from the shallow end
B. at the shaiiow end
C. at the deep end
D. can't be determined

Answer

To solve the problem step by step, let's break down the swimming pool scenario involving Aarti and Barkha.

### Step 1: Define the speeds of Aarti and Barkha
Let the speed of Aarti be \( v \) m/s. Since the ratio of their speeds is 1:2, the speed of Barkha will be \( 2v \) m/s.

### Step 2: Calculate the time taken by Aarti to reach the shallow end
The distance Aarti swims is 300 meters. The time taken by Aarti to reach the shallow end is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{300}{v} \text{ seconds} \]

### Step 3: Calculate the time taken by Barkha to reach the deep end
Barkha also swims the same distance of 300 meters. The time taken by Barkha to reach the deep end is:
\[ \text{Time} = \frac{300}{2v} = \frac{150}{v} \text{ seconds} \]

### Step 4: Include resting time
After reaching their respective ends, both swimmers rest for 6 seconds. Therefore, the total time taken by Aarti to reach the shallow end and rest is:
\[ \text{Total time for Aarti} = \frac{300}{v} + 6 \text{ seconds} \]
And for Barkha:
\[ \text{Total time for Barkha} = \frac{150}{v} + 6 \text{ seconds} \]

### Step 5: Calculate the time taken for Aarti to swim back
After resting, Aarti will swim back to the deep end. The time taken for her to swim back is again:
\[ \text{Time} = \frac{300}{v} \text{ seconds} \]
Thus, the total time for Aarti to reach the shallow end, rest, and swim back to the deep end is:
\[ \text{Total time for Aarti} = \frac{300}{v} + 6 + \frac{300}{v} = \frac{600}{v} + 6 \text{ seconds} \]

### Step 6: Calculate the time taken for Barkha to swim back
Barkha, after reaching the deep end, rests for 6 seconds and then swims back to the shallow end. The time taken for her to swim back is:
\[ \text{Time} = \frac{300}{2v} = \frac{150}{v} \text{ seconds} \]
Thus, the total time for Barkha to reach the deep end, rest, and swim back to the shallow end is:
\[ \text{Total time for Barkha} = \frac{150}{v} + 6 + \frac{150}{v} = \frac{300}{v} + 6 \text{ seconds} \]

### Step 7: Determine when they meet for the second time
To find when they meet for the second time, we need to find the time when both swimmers are back in the pool after their respective rests.

- Aarti's total time to swim back to the shallow end is \( \frac{600}{v} + 6 \).
- Barkha's total time to swim back to the shallow end is \( \frac{300}{v} + 6 \).

### Step 8: Set the times equal to find the meeting point
To find the time at which they meet for the second time, we can set the total times equal:
\[ \frac{600}{v} + 6 = \frac{300}{v} + 6 \]
This simplifies to:
\[ \frac{600}{v} = \frac{300}{v} \]
This equation is not valid, indicating that they will meet at the shallow end after their respective swims and rests.

### Conclusion
They will meet for the second time at the shallow end of the pool.