A waste water stream (flow $=2 m^3/s$, ultimate BOD$=90$ mg/l) is joining a small river (flow $=12 \: m^3/s$, ultimate BOD $=5$ mg/l). Both water streams get mixed up instantaneously. Cross-sectional area of the river is $50 \: m^2$. Assuming the de-oxygenation rate constant, $k=0.25/day$, the BOD (in mg/l) of the river water $10$ km downstream of the mixing point is

1. $1.68$
2. $12.63$
3. $15.46$
4. $1.37$