Question

If two quantities $p$ and $q$ vary inversely with each other, then:

• A. $\frac{p}{q}$ remains constant
• B. $p+q$ remains constant
• C. $p\times q$remains constant
• D. $p–q$ remains constant

Answer 1

The correct option is C

$p\times q$remains constant

Explanation for the correct answer:

Two quantities are said to be inversely proportional to each other when an increase in one causes a decrease in the other, and decrease in one causes increase in another.

It can also be stated as two quantities are inversely proportional to each other when, one quantity is directly proportional to the reciprocal of the other.

If $p$ and $q$ are inversely proportional then we can say that

$p\propto \frac{1}{q}$

Let $k$ be a constant of proportionality. Then,

$p=\frac{k}{q}$

$\Rightarrow$$p\times q=k$

Hence, $p\times q$ remains constant, so option(C) is the correct answer.