After $$150$$ days, the activity of a radioactive sample is $$5000\,dps.$$   The activity becomes $$2500\,dps$$   after another $$75$$ days. The initial activity of the sample is

Solution :
Activity of sample becomes $$2500$$  from $$5000$$  in $$75$$ days therefore its half life is $$75$$ days, so
$$\eqalign{ & R = \frac{{{R_0}}}{{{2^{\frac{{150}}{{75}}}}}} = 5000 \cr & \Rightarrow {R_0} = 5000 \times 4 = 20,000 \cr} $$