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Gain or Loss (Posted on 2003-07-05) Difficulty: 3 of 5
The minute and the hour hand of a watch meet every 65 minutes.

How much time does the watch lose or gain ?

See The Solution Submitted by Ravi Raja    
Rating: 3.1667 (6 votes)

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Solution Explanation For The Answer Comment 7 of 7 |
(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
  Posted by K Sengupta on 2007-11-22 05:08:08

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