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I gave a mental ability test today in which this question was asked.
The hour and minute hands of a clock are indistinguishable. How many minutes are there in a day (24 hours) when it is not possible to tell what time it is from the clock?
What I tried: I pondered a lot over this question... since both hands are same, the only difference lies in their speed. The hour hand turns 30 degrees in an hour and the minute hand turns a whole 360 degrees (one complete circle). So, in order to count the number of minutes, i need to calculate sum(probably) both of their rotations. The $24*60 = 1440$ of actual minute hand is to be counted, and hours hand's extra rotation has to be added.
But, here I got struck, how to proceed was a big problem.
Can someone please explain on how to solve this question in detail.