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Correct Option is 65

Little tricky question. You will not be able to use any formula in this question. Use option checking and see which ones you can eliminate logically. 

A clock hour hand every hour moves by 30◦ (360◦ /12 hours) in every hour i.e. 60 minutes (i.e. 0.5 degrees every minute). But the minute hand moves by 360◦ every 60 minutes (i.e by 6◦ every minute). 

Imagine, both the hands of the clock are over one another at a time which is possible somewhere around 8:40 and 8:45. 

Now, lets try to estimate a more specific position of the hour and minute hand by seeing what position the hour hand would have been at these two times – 8:40 and 8:45 

After, 40 minutes past 8, the hour hand will have advanced 40 minutes X 0.5 degrees per minute = 20◦ from the position of 8 AM/PM (Gap between 8-9 Am/PM is of 30◦ ). After 45 minutes, it would have advanced 22.5◦ from the position of 8 Am/pm. This means it would have completed 2/3rd of its movement from 8 AM/PM to 9 AM/PM and will be a little ahead of it. 

So, at 20◦ movement from the position of 8 Am/PM, it would have covered 3.33 minutes. At 22.5◦ , 3.75 movement. So lets safely assume that it has covered 3.5 minutes past 8:40, i.e. the time can be assumed as 8:43.5 when both hands meet. 

For them to meet again, the minute hand should meet the hour hand between 45-50 minutes, i.e. between 9:45 – 9: 50. After minute hand travelling for 45 minutes past 9, the hour hand would have definitely crossed 9:48 PM, but less than 9: 50 PM/AM. 

So the gap between the times when both meet can never be 60 minutes, or 62 minutes or 67 minutes (you can subtract and check 

Clearly the nearest answer is 65 minutes (3). 

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