Question

If a,b,c are in H.P, then $\frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}$ are in,

• A. $A.P$
• B. $H.P$
• C. $G.P$
• D. None of these.

Answer 1

Answer: (B)

$H.P$

We have,

$a,b,c$ are in $H.P$

$\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in $A.P$

On multiplying with $(a+b+c)$, we get.

$\frac{a+b+c}{a},\frac{a+b+c}{b},\frac{a+b+c}{c}$ are also in $A.P$

$\frac{a+b+c}{a}-2,\frac{a+b+c}{b}-2,\frac{a+b+c}{c}-2$ are also in $A.P$

$\frac{b+c-a}{a},\frac{c+a-b}{b},\frac{a+b-c}{c}$ are also in $A.P$

$\frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}$ are also in $H.P$

Hence option ${}^{\prime }{B}^{\prime }$ is the answer.