Correct option is B
Solution:
1. Rate of Deviation per Hour:
Clock A gets faster by 8 minutes per hour.
Clock B gets slower by 12 minutes per hour.
2. Time shown on each clock relative to the true time:
After t hours, the time deviation for Clock A is +8t minutes (it's fast).
After t hours, the time deviation for Clock B is -12t minutes (it's slow).
Let t be the true time in hours since the clocks were synchronized at 05:00 hrs.
3. Clock Readings:
Clock A shows 15:12 hrs.
Clock B shows 12:12 hrs.
4. Expressing Time on Each Clock:
Time on Clock A (fast by 8t minutes): 5:00 + t should be adjusted to show 15:12.
Thus, 300 + 60t + 8t = 912 minutes.
Time on Clock B (slow by 12t minutes): 5:00 + t should be adjusted to show 12:12.
Thus, 300 + 60t - 12t = 732 minutes.
5. Solving for t:
From Clock A: 68t = 612 or t = 612/68 = 9 hours.
From Clock B: 48t = 432 or t = 432/48 = 9 hours.
Both calculations show t = 9 hours, meaning 9 hours have passed since 05:00 hrs.
6. True Time Calculation:
The true time is 05:00 hrs + 9 hours
= 14:00 hrs.
Therefore, the correct time at that instant, when Clock A shows 15:12 and Clock B shows 12:12, is 14:00 hrs.
Hence Option (b) is correct.
