A number is first decreased by 15% and then increased by 20%. The number so obtained is 78 more than the original number. The original number is:

In a town with 30,000 professionals, teachers make up 11% of the total professionals. If 46% of teachers are male, what is the number of female teachers in the town?

In a town's professional breakdown, doctors represent 18% and clerks represent 8% of the total professionals. If the number of doctors is 3000 greater than the number of clerks, what is the total number of professionals in the town?