Half – lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be

Half-life of A, $T_{1/2\left(A\right)}=20\min$

Half-life of B,  $T_{1/2\left(B\right)}=40\min$

Initially, number of nuclei in each sample =N

Now, $80\min =4T_{1/2\left(A\right)}=2T_{1/2\left(B\right)}$

Number of active nuclei after four half-lives of A,

$N_A=\frac{N}{2^4}=\frac{N}{16}$

$\therefore$ Number of decayed nuclei of A = $N-N_A=\frac{15}{16}N$

Number of active nuclei after two half-lives of B,

$N_B=\frac{N}{2^2}=\frac{N}{4}$.

$\therefore$ Number of decayed nuclei of B = $N-N_B=\frac{3}{4}N$

$\therefore$ Required ratio = $\frac{\frac{15}{16}N}{\frac{3}{4}N}=\frac{5}{4}$