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This is a nice problem for a course of probability theory, but honestly I don't think that is a good aptitude question under this interpretation. I mean to say that I don't think that the questioner expects an answer like "Assuming that the times of arrival are indepent and uniformly distributed between 5 am and 6 am, the probability that the two enter times lie into a gap of 10 minutes is 0.3056". (Unless it is a very very very specific test.)
I'd think rather in some of the hexreader's interpretation.
Was it a spoken interview or a written test?
In the first case, if I was the questiones I would expect a request for clarification from you.
In the second case, an answer like "The probability is very high if they come together" would not be so bad.
Suppose person A enters at some arbitrary time Ta, which is within the 5-6am period, or a 60 minute period.
Then what is the prob that person B entered in a time period which is +/- 10 min of this time Ta, subject to the 5-6am limits.
Now thats a duration of 20 minutes if 5.10am < Ta < 5.50am
And a reducing period, minute for minute, for Ta within the 1st 10 minutes & last 10 minutes.
So as a simplistic answer, i'd say 20/40 + 5/20 = 0.5.
Wow... its a 50% probability ! Heh...
On a more serious note - this seems to be a puzzle in queueing theory, where arrival times of events is usually modeled by Poisson distribution. Or not. I forget now how to play with those equations.... but yes, definitely an unusual question for a standard aptitude test.