A U$-$tube whose arms are open to the atmosphere is filled with $3$ different liquids. Ratio of height for liquid $R$ to water is $3$ at left arm while ratio of height for liquid $Q$ to water is $2$ at right arm. If density for liquid $Q$ is $820k\frac{g}{m^3}$ and density for liquid $R$ is $795k\frac{g}{m^3},$ calculate the height of liquid $Q$ and water at the right arm.

$(10$ marks$)$