For sample 1 we can write,
N1=No1e−λ1t
N2=No2e−λ2t
Given that at a particular time t N1=2N2
Also given that
For sample 1,
A1=−dN1dt=No1λ1e−λ1t=5μCi
A2=−dN2dt=No2λ2e−λ2t=10μCi
Solvong above equations we get,
λ1λ2=14
half life1half life2=ln2λ1×λ2ln2=4
TS1=4TS2
⇒TS1=20 years and TS2=5 years is the possible answer.