I think you are dealing with a volume-to-volume percent concentration (#"v/v%"#), which is defined as the volume of the solute divided by the total volume of the solution and multiplied by 100%. This is mathematically described as
#"v/v%" = ("volume of solute")/("total volume of solution") * 100%#
So, in your case, you have a volume of solute equal to #50muL# and a volume of solvent, NOT of total solution, equal to #200muL#.
You add the solute to the solvent and get a total volume of solution of
#50# #mu##"L" + 200# #mu##"L" = 250# #mu# #"L"#, which means that your #"v/v"# percent concentration is
#"v/v%" = (50muL)/(250muL) * 100%= 20%#
So, essentially, you have dilluted the original #50muL# sample to 1/5th of its original concentration:
#C_("initial") * 50 muL = C_("final") * 250 muL => C_("final") = C_("initial") * (50muL)/(250muL)#
#C_("final") = C_("initial")/5#.
