It was some time between 7 and 8 PM that Sam looked at his watch. Some time later, between 10 and 11 PM, he looked again, and coincidentally, the hour hand and minute hand were exactly switched from the first time he looked. What were the two times?
(In reply to
Puzzle Answer by K Sengupta)
The first time Sam looked at his watch was p minutes past 7 pm (say)
The second time Sam looked at his watch was q minutes past 10 pm(say)
Then in accordance with the given conditions, we must have:
7 + p/60 = q/5 ..........(i)
and, 10 + q/60 = p/5 ..........(ii)
Multiplying each of (i) and (ii) by 60 and rearranging the terms, we must have:
12q - p = 420 ........(iii)
12p - q = 600 .......(iv)
Then, 12*(iii) + (iv) gives:
143q = 5640
63
=> q = 5640/143 = 39-----
143
Again, 12*(iv) + (iii) gives:
143p = 7620
41
=> p = 7620/143 = 53------
143
Consequently, the two times were:
41
FIRST: 53------ minutes past 7 PM
143
SECOND: 6
39------ minutes past 10 PM
143
Edited on August 6, 2023, 12:05 am
Explanation to Puzzle Answer
