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If on increasing $a,$ $b$ decreases in such a manner that their remains constant and positive, then $a and b$ decreases in such a manner that their remains constant and positive, then vary inversely with each other.

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Detailed Solution

If on increasing

a,

b

decreases in such a manner that their product remains constant and positive, then

a and b

vary inversely with each other.
We know that the two variables

x and y

are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

When an increase in quantity

a

results in a proportional decrease in quantity

b

and vice versa, the product of their respective values don’t change, the two quantities are said to be in inverse proportion.
i.e.

a b = k,

where

k

is constant and a positive number
Hence, if on increasing

a,

b

decreases in such a manner that their product remains constant and positive, then

a and b

vary inversely with each other.

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