In the following first order reactions $\text{ (A) }\stackrel{h_1}{⟶}$ product, $\left(B\right)\stackrel{k_2}{⟶}$ product, the ratio k1 /k2 if 90% of (A) has been reacted in time 't' while 99% of (B) has been reacted in time 2t is :

The relation of rate constants with time is given as,

$k_{1}t=\ln \left(\frac{100}{10}\right);k_2\times 2t=\ln \left(\frac{100}{1}\right)$

the ratio k1 /k2 , when 90% of (A) has been reacted in time 't' while 99% of (B) has been reacted in time 2t is,

$\Rightarrow \frac{k_1}{2k_2}=\frac{1}{2}$