Mike has a bookcase with three layers, and the proportion of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level,  books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same. 
Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part
Lower level: $$240\div6\times4=160$$,  The number of books to be added to the lower level: $$(240-160)\div2=40$$.  So, the answer is $$\text{B}$$. 