Is it necessary to instal fire damper in both supply and return duct?

no not neccesary it depends on the type of wall and area.

Yes it is definately required to install the fire dampers in Supply and Return Air ducts in order to stop the fire passsing from the fire zone to the other areas. 

Yes! Required must to avoid the unwanted things happen to the occupiers and machineries.

Wherever the duct passing through the "walls are fire rated" firedampers are required in both supply & return ducts. Fire dampers of certain rated hours installed in a supply air duct in a fire rated partition supplying air from fire zone to non fire zone, is necessary in order to prevent spreading of fire from the source that is fire hazardous zone to another room which is not a fire zone. There should be return duct at the said fire rated partition as per HVAC design, and hence to comply to the fire code return duct too needs a fire damper.

If bouth ducts goes through fire rated wall. the answer is yes

It depends on many situations sometimes it is installed on both sometimes on one. But the answer to your question is NO. IT IS NOT NECESSARY.

Regards

Hi binuraj,

Necessity of installing fire damper does not have any relation with supply or return ducts, As fire dampers are installed on both according to the requirement(Ducts passing through any enclosure which is build by fire rated materials).