The rate of steady volume flow of water through a capillary tube of length  $l$ and radius r  under a pressure difference P is  Q. Then the rate of steady flow through a series combination of the tube with another tube of same length and half the radius if the same pressure difference P is maintained across the combination is 

We know that coefficient of viscosity,  $\eta =\frac{\pi {\mathrm{Pr}}^4}{8Vl}\Rightarrow P=\frac{\eta 8Vl}{\pi r^4}$
Let $P_1,P_2$  be the pressures at the ends of the two tubes and $V_1$  be the rate of volume flow through them, then pressure difference across the first tube,  $P_1=\frac{\eta 8V_{1}l}{\pi r^4}$
Pressure difference across the second tube,  $P_2=\frac{\eta 8V_{1}l}{\pi {(r/2)}^4}$
The two tubes are connected in series. So, the total pressure,  $P=P_1+P_2$
$\Rightarrow \frac{\eta 8Vl}{\pi r^4}=\frac{\eta 8V_{1}l}{\pi r^4}+\frac{\eta 8V_{1}l}{\pi r^4}\times 16\Rightarrow Q=V_1+16V_1=17V_1=\frac{Q}{17}$
So, the correct answer is (B).