(b) That's right. On these facts, A has not given consideration in exchange for B's promise to reduce the rent. The problem is that, by the time B promises to reduce the rent, A has already painted the flat, and has apparently done so purely on his own initiative. When something has already been done before a promise is made, it cannot be later 'given' in exchange for that promise. The act already done is referred to as 'past consideration' and the general rule is that past consideration is not good consideration.
It would be different if B had promised to reduce the rent before A had painted the flat, and in return A had promised to do the painting. An exchange of promises provides good consideration. The decision would also be different if A had painted the flat at B's request with B indicating to A that he would somehow pay him. In such circumstances, the courts would treat A's performance not as past consideration but as 'executed' consideration, i.e. something done in the expectation that a binding promise to pay for it will be made sometime later. Executed consideration is sufficient to make a later promise legally enforceable.