A cantilever beam of length L is subjected to a uniformly distributed load w (load per unit length) over its whole length L and a concentrated load W (upward) at the free end. If the total downward load W_total = wL is equal to the upward concentrated load W, the deflection at the free end is:

Why is this the answer?

The downward deflection due to UDL is wL^4/8EI. The upward deflection due to point load W at the free end is WL^3/3EI. Since W = wL, the net deflection is (wL^4/8EI) - (wL^4/3EI), which is downward.

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