If `a+c`, `a+b`, `b+c` are in `G.P` and `a,c,b` are in `H.P.` where `a`,`b`,`c gt 0`, then the value of `(a+b)/(c )` is

Options

A. `3`
B. `2`
C. `(3)/(2)`
D. `4`

Answer

B

Explanation

`(b)` `a+c`, `a+b`, `a+c` are in `G.P.`
`:. (a+b)^(2)=(a+c)(b+c)`
`(a+b)^(2)=ab+c(a+b)+c^(2)`………`(1)`
`a,c,b` are in `H.P.`
`:.c=(2ab)/(a+b)`………`(2)`
From `(1)` and `(2)`
`(a+b)^(2)=(3)/(2)c(a+b)+c^(2)` ,brgt `:.2(a+b)^(2)-3c(a+b)-c^(2)=0`
`:.a+b=-(c )/(2)`(rejected)
or `a+b=2c`
`:.(a+b)/(c )=2`