Correct Answer - Option 2 : 500 l/min and 12.5 mtr

__Concept:__

**For pump:**

\(\frac{\sqrt H_1}{D_1N_1} = \frac{\sqrt H_2}{D_2N_2}\) ...(i)

\(\frac{Q_1}{D_1^3N_1} = \frac{Q_2}{D_2^3N_2}\) ...(ii)

Where, H = Head, D = Diameter, N = Speed, Q = Discharge

__Calculation:__

__Given:__

H_{1} = 50 m, Q = 1000 l/min, N_{1} = 2000 RPM, N_{2} = 1000 RPM

Using equation (i)

\(\frac{\sqrt H_1}{D_1N_1} = \frac{\sqrt H_2}{D_2N_2}\)

\(\frac{\sqrt 50}{2000} = \frac{\sqrt H_2}{1000}\)

**H**_{2} = 12.5 m

Now, using (ii)

\(\frac{Q_1}{D_1^3N_1} = \frac{Q_2}{D_2^3N_2}\)

\(\frac{1000}{2000} = \frac{Q_2}{1000}\)

**Q**_{2} = **500 l/min.**