The hardness of a ground water sample was found to be $420 \: mg/L$ as $CaCO_3$. A softener containing ion exchange resins was installed to reduce the total hardness to $75 \: mg/L$ as $CaCO_3$ before supplying to $4$ households. Each household gets treated water at a rate of $540 \: L/day$. If the efficiency of the softener is $100\%$, the bypass flow rate (expressed in $L/day$) is _________