If `x\ a n d\ y` vary inversely as each other and `(i) x=3\ ` when`\ y=8,\ ` find`\ y\ ` when`\ x=4` `(ii) x=5\ ` when`\ y=15 ,\ ` find`\ x\ ` when`\ y=12` `(iii) x=3,\ ` find`\ y\ ` when constant of variation`=900.` `(iv) y=35 ,\ ` find`\ x`when constant of variation`\ =7`.

Explanation

(i)`xy=k`
`3xx8=k`
`k=24`
Now, `x=4`
then, `4xxy=24`
`y=24/4`
`y=6`
(ii) Given `x=5` and `y=15`
then, `5xx15=k`
`k=75`
now, `y=12`
then, `x xx 12=75`
`x=75/12`
`x=25/4`
(iii) Given ,`x=3`
Constant of variation i.e `k=300`
Then ,`xy=k`
`3xxy=900`
`y=(900)/3`
`y=300`
(iv) Given `y=35`
Constant of variation i.e `k=7`
Then, `xy=k`
`x xx35=7`
`x=1/5`