Interchangeable positions of minute hand and hour hand occur when the original interval between the two hands is 60/13 minute spaces or a multiple of this.
Could anyone explain this with examples?
I learnt congruence equation from Congruence Equation -- from Wolfram MathWorld
But I have no clue what can I do with congruence equation.
I think the question is stated incorrectly. The hour hand and minute hand line up every 12/11 hours, or in other words after the minute hand has made 12/11 revolutions. The new position of the minute hand is therefore 1/11 further along than on the previous alignmemt, which works out to be 60/11 = 5.4545 minutes.
The derivation of the 12/11 figure come from this: the position of the minute hand is where t is in hours, and the position of the hour hand is . The hands line up when M is equal to H plus a multiple of :
where k = 1, 2, 3... This occurs when
Thus every multiple of 12/11 hours the hands are realigned, at which time the hands are 60/11 "minutes space" further on.