For the reactions A⟶k1B and A⟶k2C, the ratio of [B]/[C] is given by

d[B]dt=k1[A] and d[C]dt=k2[A]. Hence , d[B]/dtd[C]/dt=k1k2

d[B]dt=k1[A] and d[C]dt=k2[A]. Hence , d[B]/dtd[C]/dt=k1k2

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For the reactions $A \overset{k_{1}}{⟶} B$ and $A \overset{k_{2}}{⟶} C,$ the ratio of [B]/[C] is given by

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$r = k_{1} / k_{2}$

$r = k_{1} k_{2}$

$r = k_{2} / k_{1}$

$r = k_{1} / k_{2}^{2}$

answer is A.

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$\frac{d [B]}{d t} = k_{1} [A]$ and $\frac{d [C]}{d t} = k_{2} [A] .$ Hence , $\frac{d [B] / d t}{d [C] / d t} = \frac{k_{1}}{k_{2}}$

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