| The correct time is 12:05. Here's one way of tackling the problem:
The total number of minutes out must be 3 X 30 = 90 minutes.
If the real time were before 11:55 or out of 1:05 the total number of minutes out would exceed 90 minutes: it would in fact be more than 30 + 70 = 100 minutes
out.
So the correct time must lie either between 11:55 & 12:25 or between 12:25 and 1:05.
If the correct time is x minutes after 11.55 the total number of minutes out is: x + (30 - x) + 70 - x = 100 - x.
As this is 90, this gives x = 10 and the time is 12:05. The clocks are then out by 10 minutes, 20 minutes and 60 minutes).
[The other possibility, that of the correct time lying between 12:25 and 1:05 leads to x = 20 and a correct time of 12:45. But then the clocks would have been out by 50 minutes, 20 minutes and 20 minutes respectively, and two of the clocks would then have been the same number of minutes out, which conflicts with the wording of the question.] (Incidentally, the working is far less confusing if you wait for 5 minutes and let the clocks come to 12:00, 12:30 and 1:10!) |