For number 28. I think the red fluid's density must be LESS than the purple fluid's density, basically because blue has the greatest density.

If we draw a line at the bottom of the purple column, consider this.

Above that line, the left side is piece_of_blue (b1) + red (r1), and the right side is all purple, which we can divide into two pieces that correspond to the sizes of the piece_of_blue and red, let those pieces be p2 and p1, respectively.

Forces are balanced, so mass of r1+b1 = mass of p1+p2.

Also blue must be more dense than purple, because blue is at the bottom, so the mass of b1 > mass of p2.

So the mass of r1 must be < the mass of p1.

So the density of r1 must be < the density of p1. 

And that's it. Unless I'm missing something.



The masses of the

Michael, we don't count the pressure that the blue liquid exerts on itself - those are internal forces/pressures that cancel out. The only pressures that count are the ones exerted on the blue fluid by the red and purple fluid. And, as you pointed out, the blue fluid is the most dense as it's below the red and purple fluids.

Since the pressure exerted by the red fluid and purple fluids are equal, and the red fluid has a shorter column, it must have a greater density to balance out the taller column of purple fluid. (rho *g*h).

John