Let say density of solution is g/ml.
∵ 100 g of solution contain = 75g HCl
∴ 500g of solution contain = \(\frac{75 \times 500}{100} = 75 \times 5g\; HCl\)
∴ Number of moles of HCl = \(\frac{75\times 5}{36.5} = 10.27\, mol\)
∴ Initial concentration of HCl solution = \(\frac{10.27}{500}\times 1000= 20.55 M\)
Let say, After dilution the volume of solution become V
then,
\(V \times 0.1 = 20.55 \times 500\)
\(V = \frac{20.55\times 500}{0.1}\)
\(= 102750 \,ml\)
\(V = 102.75 \,l\)