If the equations $2 a x^2-3 b x+4 c=0$ and $3 x^2-4 x+5=0$ have a common root, then $\frac{a+b}{b+c}$ is equal to $(a, b, c \in \boldsymbol{R})$

• A

  $\frac{1}{2}$
• B

  $\frac{3}{35}$
• Correct answer
  C

  $\frac{34}{31}$
• D

  $\frac{29}{23}$

Hence, the correct answer is option: 'C'.