The density of a material in SI units is 128 kg m^-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is

To convert a measured value from one system to another system, we use
N₁u₁ = N₂u₂
where, N is numeric value and u is unit. 
We get,
$$\begin{gathered} \therefore 128.\frac{\mathrm{kg}}{{\mathrm{m}}^3}={\mathrm{N}}_2\frac{50 \mathrm{g}}{{\left(25 \mathrm{cm}\right)}^3} \left[\because \mathrm{density} =\frac{\mathrm{mass}}{\mathrm{volume}}\right] \\ \Rightarrow \frac{128 \mathrm{x} 1000\mathrm{g}}{100 \mathrm{x} 100 \mathrm{x} 100 {\mathrm{cm}}^3}=\frac{{\mathrm{N}}_2 \mathrm{x} 50 \mathrm{g}}{25 \mathrm{x} 25 \mathrm{x} 25 {\mathrm{cm}}^3} \\ \Rightarrow {\mathrm{N}}_2=\frac{128 \mathrm{x} 1000 \mathrm{x} 25 \mathrm{x} 25 \mathrm{x} 25}{50 \mathrm{x} 100 \mathrm{x} 100 \mathrm{x} 100 }=40 \end{gathered}$$