The minute and the hour hand of a watch meet every 65 minutes.
How much time does the watch lose or gain ?
(In reply to Puzzle Resolution
by K Sengupta)
The minute hand (mh) and the hour hand (hh) of ant normal clock meet at (60*t/11) minutes t o'clock for t = 1,2,..., 10; and, at 12 o'clock.
In other words, mh and hh comes together in every (60+ 60/11) = 720/11 minutes.
Thus by the problem, the given clock moves 720/11 minute marks in the time it takes an ordinary clock to move 65 minute marks.
Accordingly, the given clock gains 720/11 - 65 = 5/11 minutes for every 65 minutes in a normal clock.
Consequently, he given clock gains (5/11)*(12/13)*60 = 3600/143 = (25 + 25/143) seconds for every hour on a normal clock.
Edited on November 22, 2007, 5:10 am