With Permanganate:
add the permanganate to the alkane and no reaction will occur
add the permanganate to the alkene and you will form a diol the solution will also turnfrom purple to colourless.
With bromine water:
add the bromine water to the alkane (plus you need sunlight) and you get a substitution reaction, this is a slow reaction.
add the bromine water to ther alkene and you get a addition reaction (this one does not need sunlight). This will once reacted turn damp blue litmus red. When bromine water reacts with an alkene it is decolourised, the reddish brown bromine water turns from brown to colourless.This is because alkenes are unsaturated and contain a carbon to carbon double bond.
If you did the bromine water teat ina dark place say a cupboard then the alkene would decolourise but the alkane wouldn't because it needs UV/sunlight in order to react.
When bromine water reacts with an alkane it does not decolourise