A and B decompose via first order kinetics with half lives 54 min and 18 min respectively starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 8 times that of B is (in min)

For A & B, when t = 0,  ${\left[A\right]}_0={\left[B\right]}_0=xM$
Given that  ${\left[A\right]}_e=8{\left[B\right]}_t$
For a first order reaction,  ${\left[A\right]}_t=\frac{\left[A_0\right]}{2^n}$
n = No. of half lives
$\frac{x}{2^{n_1}}=8.\frac{x}{2^{n_2}}$

$$\begin{gathered} 2^{n_2}=2^{n_1+3} \\ {n}_2=n_1+3 \\ \frac{t}{{\left(t_{1/2}\right)}_B}-\frac{t}{{\left(t_{1/2}\right)}_A}+3 t(\frac{1}{18}-\frac{1}{54})=3 \\ t\left(\frac{3-1}{54}\right)=3 \\ t=\frac{162}{2}=81\min \end{gathered}$$