Let `p, q, r epsilon R` be such that `2q = p + r` and `(2017-x)/(px) = (2017-y)/(qy) = (2017-z)/(rz)` , then the correct relation between x,y,z is

Options

A. `(x)/(x) = (x-y)/(y-z)`
B. `(x)/(y) = (x-y)/(y-z)`
C. `(x)/(z) = (x-y)/(y-z)`
D. `(x+z)/(y+z) = (x-z)/(y-z)`

Answer

C

Explanation

Let `p, q, r epsilon R` be …………..
Given
`(2017-x)/(px)=(2017-y)/(qy)=(2017-z)/(rz)`
`:' p - q = q - r given)`
`implies ((2017)/(x)-1)/(p) = ((2017)/(y)-1)/(q) = ((2017)/(z)-1)/(r )`
`implies ((2017)/(x)-(2017)/(y))/(p-q) = ((2017)/(y)-(2017)/(z))/(q-r)`
`implies (1)/(x)-(1)/(y)=(1)/(y)-(1)/(z)`
`implies (y-x)/(xy)=(z-y)/(yz) implies (x)/(z) = (x-y)/(y-z)`