Why are fungus not able to synthesise their own food?

Solution:
 

Fungi are heterotrophic organisms, that is they cannot produce their own food since they lack the pigment chlorophyll necessary for photosynthesis (unlike plants which can prepare their own food because they have chlorophyll). They can either be saprotrophs (feeding on dead decaying matter), parasites (dependent on the host organism, only the parasite benefits) or symbiotic (both the organisms benefit).