how much water must be added to a 30ml of 0.5M KOH solution to produce a solution whose concentration is 0.45M?

Answer 1

you are diluting it .5/.45 times, which means 1 part original, .1111 parts water.

what is one part?30ml.
then add 30x.1111=3.3333ml water

Check:
moles KCl=.5*.030=.0015moles
Net concentration=.0015/(.O33333)=.45M