Answer
$387\space kg/m^{3}$
Work Step by Step
We can write,
Buoyant force = Weight of the person + Weight of the jacket
$F_{B}=W_{P}+W_{J}-(1)$
According to the principle of Archimedes, we can write
$F_{B}=W_{W}=V_{W}\rho_{w}g$
$W_{J}=V_{W}\rho_{w}g-W_{P}$ ; Let's plug known values into this equation.
$W_{J}=[(3.1+6.2)\times10^{-2}m^{3}]1000\space kg/m^{3}g-81\space kg\space g=12\space g\space kg$
mass of the jacket = $\frac{12g\space kg}{g}=12\space kg$
Density of the jacket = $\frac{x12\space kg}{3.1\times10^{-2}m^{3}}=387\space kg/m^{3}$
