x varies directly with y and inversely with z if y y =4 ,z=5, then x=3 . Again ,if y=16 , z=30 , then find the value of x .

Explanation

x varies directly with y and inversely with z.
`therefore x prop y/z rArr x=k .y/z ……..(1) (where k ne0= variation cosntant )`
As per question , if y=4 ,z =5 , then x =3 .
`therefore ` from (1) we get , 3 =k. `4/5 or , k =(15)/(4)`
Then (1) becomes . x `(15)/(4) .(y)/(z) .........(2)`
Now , putting y =16 and z =30 in (2) we get , x `(15)/(4)xx(16)/(30) or , x =2 `
Hence the required value of x =2