Samples of two radioactive nuclides, $X$ and $Y$, each have equal activity A at time $t=0.$ $X$ has a half-life of $24$ years and Y a half-life of $16$ years. The samples are mixed together. What will be the total activity of the mixture at $t=48$ years?

The correct option is D $\frac{3}{8}{A}_0$
If initial activity is $A_0$
After '$n$' half lifes, activity would reduce to $\frac{A_0}{2^n}$ because number of nuclei would reduce by that much.
In $48$ hours, substance $X$ would undergo two half lives.
Its new activity would become $\frac{A_0}{4}$
Substance $Y$ would undergo three half lives.
Its new activity would become $\frac{A_0}{8}$
The total activity would be the sum:
$\frac{A_0}{4}+\frac{A_0}{8}=\frac{3A_0}{8}$