1. Given

   Two capacitors $C_1$ and $C_2$ are initially charged to potentials: $V_1=120\text{ V}, \qquad V_2=200\text{ V}$

   We are told that by connecting them together, the final potential on each can be made zero.

2. Interpretation

   For the final common potential to be zero, the algebraic sum of charges must be zero when they are connected with opposite polarities.

   Initial charges: $Q_1=C_1V_1=120C_1$ $Q_2=C_2V_2=200C_2$

   Since the final potential is zero, the net charge after connection must be zero: $Q_1-Q_2=0$ or $120C_1=200C_2$

3. Simplify

   Divide by $40$: $3C_1=5C_2$

4. Match with options

   This corresponds to: Option B: $3C_1=5C_2$

5. Verification of other options

   • A: $5C_1=3C_2$ — incorrect
   • B: $3C_1=5C_2$ — correct
   • C: $3C_1+5C_2=0$ — impossible for positive capacitances
   • D: $9C_1=4C_2$ — incorrect

Therefore, the correct answer is B.