Consider the following first order competing reactions:
$X \overset{k_{1}}{\to} A + B a n d Y \overset{k_{2}}{\to} C + D$
if 50% of the reaction of X was completed when 96% of the reaction of Y was completed, the ratio of their rate constants $(k_{2} / k_{1})$ is:

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Detailed Solution

$\begin{array}{l} K_{2} = \frac{1}{t} l n \frac{100}{4} ........ (i) \\ K_{1} = \frac{1}{t} l n \frac{100}{50} ........ (i i) \\ \frac{K_{2}}{K_{1}} = \frac{l n 25}{l n 2} = 4.65 \end{array}$

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