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**