c
\(k _{ A }=\frac{\ln 2}{100} ; k _{ B }=\frac{\ln 2}{50}\)

\(A _{ t }= A _{0} \times e ^{- k _{ A } t }\)

\(A _{ t }= A _{0} \times e ^{\left(\frac{-\ln 2}{100} \times t \right)}\)

\(B _{ t }= B _{0} \times e ^{\left(\frac{-\ln 2}{50} \times t \right)}\)

\(A _{0}= B _{0}\)

\(At =4 B _{ t }\)

\(e ^{-\frac{\ln 2}{100} \times t }=4 \times e ^{-\frac{\ln 2}{50} \times t }\)

\(e ^{\frac{\ln 2}{100} \times t}=4\)

\(e ^{\frac{\ln 2}{100} \times t}=4\)

\(\frac{\ln 2}{100} \times t=\ln 4=2 \ln 2\)

\(t=200 \,sec\)