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 angle made by hour hand & seconds hand at any time t seconds is
360*t/(60*60*12) & 360*t/60 respectively
angle between the seconds hand & hour hand is
t*719/120
if seconds hand is on a second mark then t is amultiple of 6 lets say 6*n
if the seconds hand is 18 marks ahead than the angle difference is 108
hence
n*719/20 = y*360 +108
for it to be possible n has to be a multiple of 20
let us say x*20 therefore
x*719 = y*360 +108
since any number ending in 9 when multiplied with another number will give a number ending in 8 only if the other number ends in 2 & since there are only 60*60*12 seconds in 12 hrs the value of x cannot be more than 360
Trying numbers ending with 2 we get 252 as solution for x
hence t=252*20*6 =30240 seconds
or 8 hrs & 24 mins

Posted by salil
on 20060220 07:28:19 