The half-life of a radioactive substance is 20 minutes. The time (in minutes) taken between 12% decay and 78% decay of the same radioactive substance is

$\begin{array}{l}{N}_0=\text{ Nuclei at time }t=0\\ N_1=\text{ Remaining nuclei after }12\%\text{ decay }\\ =(1-0.12)N_0=0.88N_0\\ N_2=\text{ Remaining nuclei after }78\%\text{ decay }\\ N_2= \left(1-0.78\right)N_0=0.22N_0\end{array}$

Hence, two half life is required between 12 % decay and 78 % decay of a radioactive substance. N₂ =N₁/4

$\therefore \text{ Time taken }=2{\tau }_{1/2}=2\times 20 \min =40 \min$