An open-ended U-tube of uniform cross-sectional area contains water
\((density\) \(10^{3} \,kg\, m ^{-3} )\). Initially the water level stands at \(0.29 \,m\) from the bottom in each arm Kerosene oil (a water-immiscible liquid) of density \(800 \,kg\, m ^{-3}\) is added to the left arm until its length is \(0.1 \,m\), as shown in the schematic figure below .The ratio \(\left(\frac{ h _{1}}{ h _{2}}\right)\) of the heights of the liquid in the two arms is