What time is it if the second hand is exactly on a second mark, and exactly 18 second marks ahead of the hour hand?

 

The required time is 24 minutes past 8.<o:p> </o:p>

Explanation<o:p> </o:p>

Since the second mark and the minute mark are the same and the hour hand is exactly on the second mark P (say) it follows that the current time is 12R Minutes past K hours where P = 5*K + R  for R=0,1,2,3,4. Since R is a whole number , the second hand [ at (P+18) second mark] must be situated precisely on the 60 second mark ,giving

P+18 = 60 => P = 42.Now 42 = 5*8+2 giving R=2 so that 12R= 24. Accordingly , the current time is 24 Minutes  past 8.

<o:p> </o:p>

Edited on July 5, 2005, 5:35 am

Posted by K Sengupta on 2005-07-05 05:34:47