In an election between two candidates, one got 55% of the total valid votes, and 20% of the total polled votes were invalid. If the total number of votes polled was 7,500, then what is the number of valid votes in favour of the other candidate?

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?