I'll have a go, but I might be wrong - it's a long time since I did dilutions! As with all chemistry problems, it's a good idea to work out how many moles you have (or need). Moles NaOH needed = conc. x vol. = 0.1 x 50/1000 = 0.005 moles
The NaOH solution provided is 1mol/dm3 . How much of this solution do we need to provide 0.005 moles? Vol. = mol/conc = 0.005/1 = 0.005 dm3 = 5cm3
We now have our 0.005 moles of NaOH. We want a concentration of 0.1 mol/dm3 How much volume do we need for this?
Vol. = mol/conc = 0.005/ 0.1 = 50cm3
The total volume of our solution must be 50cm3 , but don't forget that we already have 5cm3 of NaOH in our volumetric flask.
We must now add 45cm3 of water to make the required volume.