The minute and the hour hand of a watch meet every 65 minutes.

How much time does the watch lose or gain ?

In a normal watch:
Angular velocity of hour hand = 30 deg/hr
Angular velocity of minute hand = 360 deg/hr

If hour hand and minute hand start together:
let angle covered by hour hand before meeting minute hand next, be x deg.
In the same time, the minute hand would have travelled 360+x deg

Now, (360+x)/360 = x/30
Hence, x = 360/11 deg

Therefore, time elapsed between hour hand and minute hand meetings
= 360/11/30 hr
= 1 hr, 5 min, & 27.2727.. sec

Since, in the watch in question, the two hands meet every 65 minutes instead, it must be gaining 27.2727.. sec in every 1 hr & 5 min,
which is a litte over 25 sec per hour (25.174825.. sec/hr to be precise)

Posted by Sanjay on 2003-07-05 08:37:48