Law of Radioactive Decay question from JEE Main 2023 (29 Jan, Shift 2)

Answer: (b)

1. Moles at start: A: $\dfrac{320}{16} = 20$ mol, B: $\dfrac{320}{32} = 10$ mol.
2. In 2 days A goes through 2 half lives: $20 \times \dfrac{1}{4} = 5$ mol.
3. B goes through 4 half lives: $10 \times \dfrac{1}{16} = 0.625$ mol.
4. Total atoms $= 5.625 \times 6.02 \times 10^{23} \approx 3.38 \times 10^{24}$
5. So the answer is (b) $3.38 \times 10^{24}$.