Boiling point of a 2 % aqueous solution of a nonvolatile solute A is equal to the boiling point of 8 %…

For $\mathrm{A}$ : $100\mathrm{gm}$ solution $\to 2\mathrm{gm}$ solute $\mathrm{A}$ $\therefore$ Molality $=\frac{2/{\mathrm{M}}_{\mathrm{A}}}{0.098}$

For $\mathrm{B}$ : $100\mathrm{gm}$ solution $\to 8\mathrm{gm}$ solute $\mathrm{B}$ $\therefore$ Molality $=\frac{8/{\mathrm{M}}_{\mathrm{B}}}{0.092}$

$\because {\left({\mathrm{\Delta T}}_{\mathrm{B}}\right)}_{\mathrm{A}}={\left({\mathrm{\Delta T}}_{\mathrm{B}}\right)}_{\mathrm{B}}$

$\therefore$ Molality of $\mathrm{A}=$ Molality of $\mathrm{B}$

$\therefore \frac{2}{0.098{\mathrm{M}}_{\mathrm{A}}}=\frac{8}{0.092{\mathrm{M}}_{\mathrm{B}}}$

$\frac{2}{98}\times \frac{92}{8}=\frac{{\mathrm{M}}_{\mathrm{A}}}{{\mathrm{M}}_{\mathrm{B}}}$

$\frac{1}{4.261}=\frac{{\mathrm{M}}_{\mathrm{A}}}{{\mathrm{M}}_{\mathrm{B}}}$

$\therefore {\mathrm{M}}_{\mathrm{B}}=4.261\times {\mathrm{M}}_{\mathrm{A}}$