An optically active substance 'A' is decomposing into optically active substance 'B' and 'C' as :

$A\stackrel{k={10}^{-3}{{\min }^{-1}}^{ }}{⟶}2B+C$The specific rotations of A, B and C are + 40°, + 10° and- 30° per mole, respectively. Initially 'A' and 'C' were present in 4 : 3 mole ratio. After what time (in min), the sample becomes optically inactive?

(Given :$\left.\ln \frac{7}{5}=0.34,\ln \frac{20}{13}=0.43\right]$