The solubility of iodine in water increases in the presence of

Iodine has the least affinity for water and is only slightly soluble in it. However, it dissolves in 10% aq. solution of KI due to the formation of a complex ion i.e. $I_3^{-}$.

${\mathrm{I}}_2+\mathrm{KI}\rightleftharpoons {\mathrm{KI}}_3\hspace{0.33em}\mathrm{or}\hspace{0.33em}{\mathrm{I}}_2+{\mathrm{I}}^{-}\rightleftharpoons {\mathrm{I}}_3^{-}\mathrm{\hspace{0.33em}}\left(\mathrm{complex} \mathrm{ion}\right)$