Since the regular interval of alarms are 50s and 48s.

So both alarms ring together after x sec., where x is LCM of 50 and 48.

Now LCM(50, 48) =1200

So both alarms ring together after 1200 sec.

Or, both alarms ring together after 20 min. (by dividing 60)

Now, since they beep together at 12 noon,

So next time they beep together at 12:20 PM.