The magnitude of a physical quantity remains constant regardless of the system of units used. Thus, $n_1 u_1 = n_2 u_2$. The dimensional formula for density is $[M L^{-3}]$. We have $n_1 = 4$, $M_1 = 1\text{ g}$, $L_1 = 1\text{ cm}$. In the new system, $M_2 = 100\text{ g}$, $L_2 = 10\text{ cm}$. Using the relation $n_2 = n_1 \left[\frac{M_1}{M_2}\right]^a \left[\frac{L_1}{L_2}\right]^b$, where $a = 1$ and $b = -3$: $n_2 = 4 \times \left[\frac{1\text{ g}}{100\text{ g}}\right]^1 \times \left[\frac{1\text{ cm}}{10\text{ cm}}\right]^{-3}$ $n_2 = 4 \times \left(\frac{1}{100}\right) \times (10)^3 = 4 \times \frac{1000}{100} = 40$. Therefore, the value of density in the new system is $40$.