The amine which reacts with $p$-toluenesulphonyl chloride to give a clear solution which on acidification gives insoluble compound is a primary amine such as ethyl amine $C _{2} H _{5} NH _{2}$.
$C _{2} H _{5} NH _{2}+ CH _{3}- C _{6} H _{4}- SO _{2}- Cl \xrightarrow{ OH ^{-}} CH _{3}- C _{6} H _{4}- SO _{2}- NHC _{2} H _{5}$
$\xrightarrow{ KOH} CH _{3}- C _{6} H _{4}- SO _{2}- N ^{-} C _{2} H _{5} K ^{+} \xrightarrow{ H ^{+}}CH _{3}- C _{6} H _{4}- SO _{2}- NHC _{2} H _{5}$
It is Hinsberg's test used to distinguish between primary, secondary and tertiary amine.