An observation is made on a clock and it is found that the hour hand is placed exactly at the minute mark while the minute hand is six minutes ahead it. After some time, the clock is observed again and it is found that the hour hand is exactly on another minute mark while the minute hand is seven minutes ahead of it.
Analyzing this data, can you calculate the total time that has elapsed between the two observations?  Choose the correct answer:
A) 2hr 11min  B) 1hr 11min  C) 3hr 11min  D) 2hr 15min  E) 3hr 21min
A   Now this question cannot be solved unless you know a fact i.e. the hour hand is exactly on the minute mark five times every hour - on the hour, 12 minutes past hour, 24 minutes past hour, 36 minutes past hour and 48 minutes past hour.   Denoting the number of hours with X and the number of minutes as Y, let us begin with the calculation.   When we have the hour hand on the minute mark, the position of hour hand:   5X + Y/12   And the position of the minute hand = Y   When the first observation was taken,   Y = Y = 5X + Y/12 + 6   Or, 60X = 11Y - 72.   With the given facts, we know for sure that Y can only be 0, 12, 24, 36 or 48.   According to which, the possible values for X and Y can be 1 and 12 respectively. Thus the time must be 1:12 when the first observation was taken.   Similarly, in the second observation, let's make the equation:   60X = 11Y - 84   Here, the possible values for X and Y here are 3 and 24 respectively. According to this, the time is 3:24 for sure.   From 1:12 to 3:24, two hours and eleven minutes have passed.
<result>A</result>
An observation is made on a clock and it is found that the hour hand is placed exactly at the minute mark while the minute hand is six minutes ahead it. After some time, the clock is observed again and it is found that the hour hand is exactly on another minute mark while the minute hand is seven minutes ahead of it.
Analyzing this data, can you calculate the total time that has elapsed between the two observations?