Question

If $a,b$ and $c$ are nonzero real numbers such that $ab=2(a+b),bc=3(b+c)$ and $ca=4(c+a)$ then the value of $5a+7b+c$ is :

• A. $18$
• B. $72$
• C. $108$
• D. $120$

Answer 1

The correct option is B

$72$

$\Rightarrow \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{13}{24}$
Now from $\left(i\right),\left(ii\right)$ and $\left(iii\right)$
$\Rightarrow \frac{1}{a}=\frac{5}{24},\frac{1}{b}=\frac{7}{24},\frac{1}{c}=\frac{1}{24}\therefore 5a+7b+c=72$