If ` x prop 1/y ` and `y prop 1/z k,` then find if there be any relation of direct or inverse variation between x and z .

Explanation

`x prop 1/y rArr x= k_1, 1/y ` (where `k_2 ne 0=` variation constant )……… (1)
Again `y prop 1/z rArr y k_2 .1/z ` (where `k_2 ne 0 = ` variation constant d………….. (2) h
Now, putting `y= k_2. 1/z ` in (1) we get . `x= (k_1)/(k_2. 1/z)= k_1/k_2.z =k.z [ " when " k = k_1/k_2 ne 0 ] `
`therefore x = k.z ` (where `k ne 0` = variation cantant )
`therefore ` x and z are in direct variation.