No absolute quantities have been given so it will only be possible to give relative proportions.
However, the problem will first be "solved" arithmetically then algebraically.
Let's say there are 160 items (say, cereal) already in the other warehouse.
If as a result of adding the transferred items the warehouse stock increases by 20% then that will add 20% of 160=32 items to the warehouse. Therefore, the quantity of teabags will be 5/16 of 32=10 items and the quantity of candy will be 11/16 of 32=22 items. So we have 160+32=192 items in the warehouse, 10 of which are teabags and 22 are candy. The fraction of teabags is 10/192=5/96 and the fraction of candy is 22/192=11/96. The ratio teabags to candy remains at 5:11. Cereal now takes up 160/192=5/6 of the items in the warehouse. The ratio cereal:teabags:candy=160:10:22=80:5:11.
Algebraically, let Q=the number of items already in the warehouse. 20% of this is Q/5. (5/16)(Q/5)=Q/16 teabags and (11/16)(Q/5)=11Q/80 candy. Total items in the warehouse=Q+Q/16+11Q/80=6Q/5. The fraction of teabags=(Q/16)/(Q+Q/5)=(1/16)(5/6)=5/96 (5.2%) and candy=(11Q/80)/(Q+Q/5)=(11/80)(5/6)=11/96 (11.5%) and remaining items=5/6 (83.3%). The ratio of teabags to candy remains at 5:11.
The final ratio of all goods is: Q:Q/16:11Q/80=1:1/16:11/80=80:5:11.