A flask contains a mixture of compounds A and B . Both compounds...

{C}_{t} = {C}_{0}{e}^{- kt}$</p><p>${k}_{A} = \dfrac{\ln 2}{300}$\left(k = \dfrac{\ln 2}{{T}_{1/2}}\right)$

${k}_{B} = \dfrac{\ln 2}{180}$

${\left({C}_{t}\right)}_{A} = {\left({C}_{0}\right)}_{A}{e}^{- {k}_{A}t}$

${\left({C}_{t}\right)}_{B} = {\left({C}_{0}\right)}_{B}{e}^{- {k}_{B}t}$

$\dfrac{{\left({C}_{t}\right)}_{, B}}{\left({C}_{t}\right), A} = \dfrac{{\left({C}_{0}\right)}_{, B}}{\left({C}_{0}\right), A} \times {e}^{\left({k}_{A} - {k}_{B}\right)t}$

$\dfrac{1}{4} = {e}^{\left({k}_{A} - {k}_{B}\right)t}$

$ln\dfrac{1}{4} = \left[\dfrac{\ln 2}{300} - \dfrac{\ln 2}{180}\right]t$

$- 2\ln 2 = \left[\dfrac{\ln 2}{300} - \dfrac{\ln 2}{180}\right]t$

$2 = \left(\dfrac{120}{180 \times 300}\right)t$

$t = \dfrac{2 \times 180 \times 300}{120} = 900sec$