Hydrostatics, find length of kerosene column in U tube

[Ishraq Begum]

Homework Statement

A glass tube is bent into a U shape. Water is poured into the tube until it sands 12 cm high on each side. Kerosene (density = 870 kg/m³) is added slowly to one side until water on the other side raises 5 cm. What is the length of kerosene column?

Homework Equations

(ρhg)₁ = (ρhg)₂

The Attempt at a Solution

Taking h₁ = 17 cm
then h₂ = (17 ⋅ 1000) / 870
so, h₂ = 19.5
but the answer in the textbook is given as 11.5

 

[gneill]

In the end, is one side purely water and the other purely kerosene? Make a sketch.

 

[Ishraq Begum]

In the end, is one side purely water and the other purely kerosene? Make a sketch.

https://ibb.co/iVWqXR
It is something like this.

 

[gneill]

https://ibb.co/iVWqXR

It is something like this.

Okay, and do your calculations reflect that scenario?

 

[Chestermiller]

There are 17 cm of water on one side, and only 7 cm of water on the other side, with h cm of kerosene above the water on that side. What is the pressure at the bottom, as determined by the heights of the fluids on the two sides sides?