QUESTION $5-$ TEMPERATURE AUTOMATIC CONTROL $(14$P$)$

A water level control system is given in the figure. When the flow rate of the linear control valve is $5\frac{m^3}{h}$ and the outlet flow rate is $5\frac{m^3}{h},$ the water level is at the required height. In this case, the output of the system working with a proportional controller is $50\%$ and the gain is $10.$ What will be the controller output and offset values when the output flow rate changes to $6\frac{m^3}{h}?$

Tip: For a linear control valve, the control output varies linearly with flow rate. So$,$ start with this idea; If an output flow rate of $5\frac{m^3}{h}$ corresponds to $50\%$ of the controller output, please find what value the controller output will show for a flow rate of $6\frac{m^3}{h}.$