While blood of a wrong group administered to a person results in complications, sometimes even death, how does a mosquito, which consumes blood from people of different blood groups not suffer the same consequences?

Answer 1: 

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During a blood transfusion in humans, donor blood enters into the recipient's circulatory system directly. If there is any degree of mismatch between the donor and recipient's blood group, an acute transfusion haemolytic reaction (ATHR) takes place. This is an accelerated destruction of red blood cells in a transfused recipient occurring during or within 24 hours after a transfusion. The destruction results from an interaction between existing antibodies in the recipient and antigens in transfused red cells. The reaction is type II hypersensitivity reaction. Cross matching of donor and recipient samples is done to prevent these catastrophes. Reactions that we see in humans do not occur in mosquitoes, as the blood does not enter the circulatory system at any stage. In a blood sucking species like the mosquito, the blood meal is to facilitate egg development. Anautogenous female mosquitoes feed on blood (0.001 - 0.01ml) that is transported directly into the stomach of the mosquito. Egg development is induced by the expansion of the stomach. Ingestion of blood stimulates the production of a series of proteolytic enzymes (including trypsins and serine proteases). The digested protein helps the eggs to mature prior to being deposited. The ingested blood does not serve as a source of nourishment. Some species pass clear urine during and after feeding, but others excrete apparently unchanged blood out of the body.

Answer 2: 

In the case of mosquitoes the blood sucked gets into the stomach where it is digested and does not get into the circulatory system as in the case of humans. Only when it directly enters the circulatory system will antibodies be generated against an antigen or any foreign body. Only when antigen-antibody reaction takes place will agglutination occur and only then will the mosquito die. This is true for any creature. Nothing will happen if one were to consume blood of a wrong group through the enteric route.

Source: thehindu.com