A question for parliamentary scholars

In Question Period, why is the minister to whom a question is addressed not required to be the one to answer it? How is it that the Prime Minister, in particular, can avoid a question at his pleasure merely by offloading it on to some hapless member of his cabinet? Has this always been allowed? Is it in other parliamentary systems? In Britain, for example, there is Prime Minister's Question Time, where the PM has to answer all the questions. And -- are you sitting down? -- actually does.