If A varies directly proportional to C and B also varies directly proportional to C, which one of the… · ABC26GN3145

$A \alpha C$ and $B \alpha C \Rightarrow A=k C$ and $B=m C$ for some constants $k$ and $m$ $$\therefore \begin{aligned} & A+B=k C+m C=(k+m) C \Rightarrow(A+B) \alpha C . \\ & A-B=k C-m C=(k-m) C \Rightarrow(A-B) \alpha C . \\ & \sqrt{A B}=\sqrt{k C \times m C}=\sqrt{k m C^{2}}=\sqrt{k m} . C \Rightarrow \sqrt{A B} \alpha C . \\ & \frac{A}{B}=\frac{k C}{m C}=\frac{k}{m}=\text { constant. } \end{aligned}$$