A sample contains 10 ^ - 2 kg each of two substances A and B with...

Ratio of number of moles of substance in the beginning will be, $\dfrac{{\left({N}_{0}\right)}_{A}}{{\left({N}_{0}\right)}_{B}} = \dfrac{\dfrac{{10}^{- 2}kg}{{M}_{A}}}{\dfrac{{10}^{- 2}kg}{{M}_{B}}} = \dfrac{{M}_{B}}{{M}_{A}} = \dfrac{1}{2}$.

Number of half-life in $16s$ for element $A$ will be, ${n}_{A} = \dfrac{16}{4} = 4$

Number of half-life in $16s$ for element $B$ will be, ${n}_{B} = \dfrac{16}{8} = 2$

Hence, ratio of number of nuclei after $16s$ will be, $= \dfrac{{\left({N}_{0}\right)}_{A} \times {\left(\dfrac{1}{2}\right)}^{{n}_{A}}}{{\left({N}_{0}\right)}_{B} \times {\left(\dfrac{1}{2}\right)}^{{n}_{B}}} = \dfrac{1}{2} \times {\left(\dfrac{1}{2}\right)}^{4 - 2} = \dfrac{1}{8} = \dfrac{25}{100}$

Thus, value of $x$ is $25$.