HClO4 +NaOH -----> NaClO4 + H2O
moles of NaOH = (0.0832 x 50 ) /1000= 4.16 x10^-3 moles
since the mole ratio of HClO4 to NaOH is 1:1 the moles of HClO4 is also 4.16 x 10^-3 moles
volume of HClO4 is therefore = moles/ molarity
that is 4.16 x 10^-3mol/ 0.167 mol/L= 0.0249L
multiply by 1000 to convert to ml
0.0249 x 1000= 24.9 ml