Blade rock scissor, I mean water

Solution 1:

Surface tension role is significant to add more volume of displaced water so as it inclines the buoyancy. However, this volume is bigger than the volume of the razor blade. Thus, the volume of water (hence the height) will decrease.

Solution 2:

Imagine that you put the system above the balance. Let the height of water in the initial state is $h_1$ , then the balance will read the total weight as (neglect the weight of the glass. Actually, it doesn't matter the conclusion will be the same)

$F_1 = \rho_{water} g h_1 A$

Now consider the final configuration where the height of the water is $h_2$ , the balance will also read

$F_2 = \rho_{water} g h_2 A + m_{blade}g(1-\frac {\rho_{water}}{\rho_{blade}})$

Using the fact that the total weight of both configurations are the same we write

$F_1 = F_2$

since $\rho_{water} < \rho_{blade}$ then

$h_2 < h_1$

Reference: 200 More Puzzling Physics Problems