Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2008 · Marks: · Difficulty:
If $A$ varies directly proportional to $C$ and $B$ also varies directly proportional to $C$, which one of the following is not correct?
(a)$(A+B) \alpha C$
(b)$(A-B) \alpha \frac{1}{C}$
(c)$\sqrt{A B} \alpha C$
(d)$\frac{A}{B}=$ constant
Answer
Answer (as printed): B
Explanation
$A \alpha C$ and $B \alpha C \Rightarrow A=k C$ and $B=m C$ for some constants $k$ and $m$ $$\therefore \begin{aligned} & A+B=k C+m C=(k+m) C \Rightarrow(A+B) \alpha C . \\ & A-B=k C-m C=(k-m) C \Rightarrow(A-B) \alpha C . \\ & \sqrt{A B}=\sqrt{k C \times m C}=\sqrt{k m C^{2}}=\sqrt{k m} . C \Rightarrow \sqrt{A B} \alpha C . \\ & \frac{A}{B}=\frac{k C}{m C}=\frac{k}{m}=\text { constant. } \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.