b
\({\text{N}} = {{\text{N}}_{\text{0}}}{e^{ - \lambda t}}\,\)

\(\therefore\) \(0.9{N_0} = {N_0}{e^{ - \lambda  \times 5}}\)

\( \Rightarrow \,5\lambda  = \log \frac{1}{{0.9}}\,....(1)\) 

અને \({\text{x}}\,{{\text{N}}_{\text{0}}} = {N_0}{e^{ - \lambda  \times 20}}\)

\( \Rightarrow \,20\lambda  = {\log _e}\left( {\frac{1}{x}} \right).....(2)\)

સમીકરણ \((1)\)  ને સમીકરણ \((2)\) વડે ભાગતા,

\(\frac{1}{4} = \frac{{{{\log }_e}(1/0.9)}}{{{{\log }_e}(1/x)}} \)

\(= \frac{{{{\log }_{10}}(1/0.9)}}{{{{\log }_{10}}(1/x)}} = \frac{{{{\log }_{10}}0.9}}{{{{\log }_{10}}x}}\)

\( \Rightarrow \,{\log _{10}}x = 4\,{\log _{10}}0.9\,\, \)

\(\Rightarrow \,\,x = 0.658 = 65.8\% \)