Question

If $a,b,c$ are in H.P. and $ab+bc+ca=15,$ then $ca=$

• A. $5$
• B. $7.5$
• C. $3$
• D. $4.5$

Answer 1

The correct option is A $5$

$ab+bc+ca=15$
Divide the above equation by $abc,$ we get
$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{15}{abc}...\left(1\right)$

Since, $a,b,c$ are in H.P.
$\therefore \frac{1}{a}+\frac{1}{c}=\frac{2}{b}...\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$\frac{3}{b}=\frac{15}{abc}$
$\Rightarrow ac=5$