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#.