A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by t=A…

A ball of radius $\displaystyle r$ and density $\displaystyle \rho$ dropped through a viscous liquid of density $\displaystyle \sigma$ and viscosity $\displaystyle \eta$ attains its terminal velocity at time $\displaystyle t$, given by $\displaystyle t=A \rho^a r^b \eta^{\mathrm{c}} \sigma^d$, where $\displaystyle A$ is a constant and $\displaystyle a, b, c$ and $\displaystyle d$ are integers. The value of $\displaystyle \frac{b+c}{a+d}$ is $\displaystyle \_\_\_\_$.