There are two counters, each representing numbers in terms of digits at 4 places; for example 3124. The first counter has digits 0, 1, 2, 3, 4, 5 and 6; while the second counter has digits 0, 1, 2, 3 and 4.Both the counters start with a display ‘0000’ and then the right-most digit advances by 1 every second. Once it completes one full cycle, the second digit from the right advances by one digit. Once this digit completes one full cycle, the third digit from the right advances by one digit. And this continues. For example, after 4 seconds the second counter will show ‘0004’, and in the next second it will show ‘0010’. Also, after showing ‘0044’, the second counter will show ‘0100’. After approximately how many hours will the leftmost digits of both the counters advance at the same time for the first time?

1) 10 hours
2) 12 hours
3) 9 hours
4) 14 hours

• 12 hrs
  
  The leftmost digit of first counter will change after 7^3 = 343 secs
  and
  The leftmost digit of 2nd counter will change after 5^3 = 125 secs
  
  LCM of 125 and 343 = 42875 ( approx 12 hrs)
• 11 years agoHelpfull: Yes(0) No(0)