Atransformer has a primary coil with 300 turns and a secondary coil with 600 turns. if the output voltage is 75 volts, what is the input voltage?

In a properly designed and operated transformer, the ratio of
the primary to secondary coil voltages is the same as the ratio of
primary to secondary coil winding turns. 

Since the secondary has twice as many turns as the primary has,
the secondary voltage is also double the primary voltage.

            75 volts  =  (2) x (primary voltage)

           Primary voltage  =  37.5 volts  AC  (transformers can't handle DC)