How Often Do the Hands of a Watch Meet Incorrectly?

[viren_t2005]

The minute and hour hand of a watch meet every 65 minutes. How much does the watch lose or gain and by how much?

 

[vaishakh]

I assume your question is same as understood by me.
Calculate the relative velocity of minute hand with respect to hour hand. When hour hand moves 5 minutes minute hand moves 60 minutes. thus the relative velocity is 360 deg corresponding to 30 deg. thus the angular relative velocity of minute hand is 12 times that of hour hand, in one minute as the minute hand moves 6deg the hourhandmoves 1/2 deg, and hence minute hand gains 11/2 deg in 1 minute. Thus after 1 meet, the minute hand and the hour hand should meet after 720/11mins. But they meet after 65mins. Thus the differencethat watch gained in the given interval is 5/11mins.