In 8 minute A fill 1 unit volume of the cistern
In 1 minute A fill $\frac{1}{8}$ unit volume of the cistern
In 12 minute B fill 1 unit volume of the cistern
In 1 minute B fill $\frac{1}{12}$ unit volume of the cistern
In 16 minute C fill 1 unit volume of the cistern
In 1 minute C fill $\frac{1}{16}$ unit volume of the cistern
so if all the three pipes A,B,C open together then in 1 minute it can fill ,
$\frac{1}{8}+\frac{1}{12}+\frac{1}{16}$ part of the cistern
so, A,B,C together $\frac{13}{48}$ unit cistern in 1 minute
so to fill the 1 unit total it will take time $\frac{48}{13}$ minute =3.7 minute
so correct answer is 3.7 minutes.(A)