what would be the molarity of a KOH solution if 15 mL of the solution required 22.3 mL of 0.085 M HCl to react with the base? 

KOH + HCl ==> H2O + KCl

moles HCl = M x L = ??
Convert moles HCl to mols KOH using the coefficients in the balanced equation.
Then MKOH = moles KOH/L KOH.