Question

If y varies inversely with x and y triples, then what happens to x?

Answer 1

The value of x is reduced to one third when the value of y is tripled.

Explanation:

Here, y varies inversely with x.

⇒
`y \propto (1)/(x) \\\implies y =  (k)/(x)`

Here, k = Constant of Proportionality.

⇒ k = x y .......... (1)

Now, given y' = 3 y

to find the value of x'

Putting the value in

`y ' =  (k)/(x')  \implies 3y=  (k)/(x')\\\implies  k = 3yx'`

or, k = 3 y x '.......... (2)

From above statement (1) and (2)

⇒ xy = 3yx'

or, x ' = x/3

Hence, the value of x is reduced to one - third when the value of y is tripled.