Question

A 5 g igal reguires addinng 8.6 ml diluent to get concentration of 250 mg/ml. The powder volume is __ ml a.9.3 b.10.6 c.11.4 d.12.8

Does the powder form a solution or a colloid? IT makes a big difference. In solutions, the sum of the powder volume and the solvent volume seldom equals the solution volume: the solute finds a way to "fit" inside the solvent particles.

Now if the powder is a colloid, often the volumes do add. In this case, I don't see that any of the answers are correct.
Powder volume + 8.6=total
Powder mass=500mg

concentration= 500mg/(8.6 +PV)=250/1
which has no solution.

Answer 1

5 gm/X=250mg/1ml 5gm=5000mg
5000mg/X=250mg/1 ml where X=final volm
5000/250=X
X=20ml
you added 8.6 ml so difference is
20-8.6=11.4ml powder vol