If `a ,b , a n dc` are in G.P. and `x ,y ,` respectively, are the arithmetic means between `a ,b ,a n db ,c` , then the value of `a/x+c/y` is `1` b. `2` c. `1//2` d. none of these

Options

A. 1
B. 2
C. `1//2`
D. none of these

Answer

B

Explanation

Given `b^(2)=ac and x=(a+b)/2,y=(b+c)/2`. Therefore
`a/c+c/y=(2a)/(a+b)+(2c)/(b+c)`
`=(2a(b+c)+2c(a+b))/((a+b)(b+c))`
`=2(2ac+ab+bc)/(ab+ac+b^(2)+bc)`
`=2(2ac+ab+bc)/(2ac+ab+bc) (becauseb^(2)=ac)`
=2