Principle of estimation

In sulphur estimation, all the sulphur present in the organic compound is finally converted into $\mathrm{BaSO_4}$.

Since 1 mole of $\mathrm{BaSO_4}$ contains 1 mole of sulphur, the mass of sulphur can be obtained from the mass of $\mathrm{BaSO_4}$.

Molar mass of $\mathrm{BaSO_4}$

$M(\mathrm{BaSO_4}) = 137 + 32 + 4(16) = 137 + 32 + 64 = 233\ \mathrm{g\,mol^{-1}}$

Mass of sulphur present in 466 mg of $\mathrm{BaSO_4}$

From stoichiometry,

$233\ \mathrm{g\ of\ } \mathrm{BaSO_4} \text{ contains } 32\ \mathrm{g\ of\ S}$

Therefore,

$466\ \mathrm{mg\ of\ } \mathrm{BaSO_4} \text{ contains } \frac{32}{233}\times 466\ \mathrm{mg\ of\ S}$

Since $466 = 2 \times 233$,

$\text{Mass of S} = \frac{32}{233}\times 466 = 64\ \mathrm{mg}$

Percentage of sulphur in the compound

Mass of organic compound taken = $160\ \mathrm{mg}$

$\%\,S = \frac{\text{mass of S}}{\text{mass of compound}}\times 100$

$\%\,S = \frac{64}{160}\times 100 = 40\%$

Final answer

$\boxed{40}$