The direct conversion of A to B is difficult, hence it is carried out by the following shown path $\mathrm{A}\to \mathrm{C}\to \mathrm{D}\to \mathrm{B}$

Given, ${\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{C}}=50\mathrm{eu},,{\mathrm{\Delta S}}_{\mathrm{C}\to \mathrm{D}}=30$ eu and,${\mathrm{\Delta S}}_{\mathrm{B}\leftrightarrow \mathrm{D}}=20$ eu, Where eu is entropy unit, then , ${\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{B}}$ is

From the given reaction sequence,

$\begin{array}{l}\mathrm{A}\to \mathrm{C}, {\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{C}}=50\mathrm{eu}\\ \mathrm{C}\to \mathrm{D}, {\mathrm{\Delta S}}_{\mathrm{C}\to \mathrm{D}}=30\mathrm{eu}\\ \mathrm{B}\to \mathrm{D}, {\mathrm{\Delta S}}_{\mathrm{B}\leftrightarrow \mathrm{D}}=20\mathrm{eu}\end{array}$

On adding (i) \  (ii) and subtracting (iii) from it, we get,

$\mathrm{A}\to \mathrm{B} {\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{B}}={\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{C}}+{\mathrm{\Delta S}}_{\mathrm{C}\to \mathrm{D}}-{\mathrm{\Delta S}}_{\mathrm{B}\leftrightarrow \mathrm{D}}$

Thus, ${\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{B}}=(50+30-20)\mathrm{eu}$

$\Rightarrow {\mathrm{\Delta S}}_{\mathrm{A}\to \mathrm{B}}=60\mathrm{eu}$

Hence, option (B) is correct.