If 0.10 mg Fe is diluted in a 50 mL flask, what is the concentration of the resulting solution? What volume of the resulting solution is needed to prepare 25.0 mL of a dilute sample solution with a concentration of 0.30 ppm Fe?

Answer 1

"What is the concn of the resulting solution" is an open ended question. What units? The easy answer is it's 0.1 mg/50 mL but that probably isn't the unit you want.
Since you want to prepare a dilute solution in ppm I thin the answer probably should be in ppm
1 ppm = 1 mg/L so all we need to do is to convert 0.1 mg/50 mL to mg/L.
That's 0.1 mg x (1000/50) = 2 mg/L = 2 ppm.
Then use the dilution formula of
c1v1 = c2v2
0.30*25 = 2*v2
v2 = ?