Given that a mass N of elements A and B exists, then:
For element A, after 100 years, we have A of mass N/2 remaining
After 200 years, we have A of mass $\frac{1}{2}\times \frac{N}{2}$ = $\frac{N}{4}$
For element B, after 50 years, we have B of mass N/2 remaining
After 100 years, we have B of mass $\frac{1}{2}\times \frac{N}{2}$ = $\frac{N}{4}$
After 150 years, we have B of mass $\frac{1}{2}\times \frac{N}{4}$ = $\frac{N}{8}$
After 200 years,we have B of mass $\frac{1}{2}\times \frac{N}{8}$ = $\frac{N}{16}$
Ratio: $(\frac{N}{4}:\frac{N}{16})$
=$4:16$ = $1:4$