Find the density of liquid Y 
While solving the question, I had some confusion, that we know net pressure at equal depths must be equal in fluids so if we try to equate the pressures at depth of 8cm (instead of the conventional 10 cm) We get the density of liquid y same as the density of x which is supposed to be wrong. Why the liquid law is getting violated?
(please correct me if I am going wrong somewhere)
 A: Your assumption that the pressure at equal depths must be equal is wrong in this case. It is true for a homogeneous liquid with no boundaries because in that case the liquid is free to flow until the pressure equalises. However in this case the liquid Y cannot flow from the left side to the right side because the mercury is in the way, and likewise liquid X cannot flow from the right side to the left side. That means they are not in equilibrium with each other and hence their pressures at the same level need not be the same.
The calculation works when we choose the level so that we are in the mercury on both sides because then we are just dealing with the pressure in a homogenous liquid. That's why we choose the level at 10cm i.e. at the X:Hg boundary on the right. Then we can say the pressure at a 10cm depth in the mercury on the right is the same as the pressure at a 10cm depth in the mercury on the left.
The problem with choosing the 8cm depth is that then we are in the mercury on the left but not in the mercury on the right.
