Rajeev and Sanjeev are too close friends Rajeev's watch gains 1 minute in an hour ans Sanjeev's watch loses 2 minutes in an hour. Once they set both the watches at 12:00 noon, with my correct watch. When will the two incorrect watches of Rajeev and Sanjeev show the same time together?

Options

A. 8 days later
B. 10 days later
C. 6 days later
D. can't be determined

Answer

To solve the problem, we need to determine when Rajeev's and Sanjeev's watches will show the same time again after starting at 12:00 noon.

### Step-by-step Solution:

1. **Understanding Rajeev's Watch:**
- Rajeev's watch gains 1 minute every hour.
- In 24 hours (1 day), Rajeev's watch will gain:
\[ 1 \text{ minute/hour} \times 24 \text{ hours} = 24 \text{ minutes} \]

2. **Understanding Sanjeev's Watch:**
- Sanjeev's watch loses 2 minutes every hour.
- In 24 hours (1 day), Sanjeev's watch will lose:
\[ 2 \text{ minutes/hour} \times 24 \text{ hours} = 48 \text{ minutes} \]

3. **Calculating the Time Gain and Loss in 10 Days:**
- In 10 days, Rajeev's watch will gain:
\[ 24 \text{ minutes/day} \times 10 \text{ days} = 240 \text{ minutes} \]
- Converting 240 minutes to hours:
\[ 240 \text{ minutes} \div 60 = 4 \text{ hours} \]
- In 10 days, Sanjeev's watch will lose:
\[ 48 \text{ minutes/day} \times 10 \text{ days} = 480 \text{ minutes} \]
- Converting 480 minutes to hours:
\[ 480 \text{ minutes} \div 60 = 8 \text{ hours} \]

4. **Finding When Both Watches Show the Same Time:**
- After 10 days:
- Rajeev's watch will show:
\[ 12:00 \text{ noon} + 4 \text{ hours} = 4:00 \text{ PM} \]
- Sanjeev's watch will show:
\[ 12:00 \text{ noon} - 8 \text{ hours} = 4:00 \text{ AM} \]
- Therefore, after 10 days, both watches will show the same time again.

5. **Conclusion:**
- The two incorrect watches of Rajeev and Sanjeev will show the same time together after 10 days.

### Final Answer:
The two incorrect watches will show the same time together after **10 days**.

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