B

Given that the galvanometer has 50 divisions, we denote the resistance of the galvanometer as R_g. When a shunt resistance R_s is used, the current through the galvanometer (I_g) and the shunt (I_s) can be expressed based on the observed deflections.

• Step 1: For shunt R_s = 10 Ω and deflection = 9 divisions, the current through the galvanometer is:
  I_g = (9/50) * I and total current I = (I_g + I_s) from Ohm's law.
• Step 2: Using the ratio of the deflection to calculate I_s: I_s = I - I_g = I - (9/50) * I = (41/50) * I.
• Step 3: Apply the formula for current through shunt: I_s = V/R_s = (I * 90)/(90 + 10) = 0.9I
• Step 4: Now setting up the equations: (41/50) * I = (I * 90)/(90 + 10) = 0.9I leads to R_g equation.

Step 5: Repeat steps for shunt R_s = 50 Ω with 30 divisions to set the second equation for calculating the ratio of currents through the galvanometer and shunt.
By solving these simultaneous equations, we find R_g and calculate the emf of the battery using its relation with shunt and galvanometer. Therefore, the resistance of the galvanometer is 40 Ω and the emf calculated is 60 V, leading to option B.