Please answer this question ....the answer as given in the book is the (e) part

Dear Student,

Here we can see that both the reactions: 

A > B, k₁ = 12.6 x 10^-4
A > C , k₂ = 3.8 x 10^-4 (It should be -4, not -5, it is a misprint.)

are 1st order. So, if both of these proceed simultaneously, then, there must be a ratio between the rate constants.

So, $\frac{k_1}{k_2}=\frac{12.6\times {10}^{-4}}{3.8\times {10}^{-4}}=3.3158$

Converting this to percentage, we have, k₂ = 23.17% and k₁ = 23.17 x 3.3158 = 76.83%

Regards