Law of Radioactive Decay question from NEET 2014 (AIPMT)

Answer: (c)

1. Every decayed X atom becomes Y, so $N_0 = N_X + N_Y$.
2. $X:Y = 1:7 \Rightarrow \frac{N_X}{N_0} = \frac{1}{8} = \left(\frac{1}{2}\right)^3$, i.e. 3 half-lives.
3. Age $= 3\times1.4\times10^9 = 4.2\times10^9$ years.
4. So the answer is (c) $4.20\times10^9$ years.