If $3^a=27^b=81^c$ and $a b c=144$, then the value of $12\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ is:

$\frac{33}{10}$

3^a = 27^b = 81^c

3^a = 3^3b = 3^4c

If we put a = 12, b = 4 and c = 3, then

3¹² = 3¹² = 3¹² [satisfied]

Now,

$12\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ = $12\left(\frac{1}{12}+\frac{1}{8}+\frac{1}{15}\right)$

$12\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ = 12(\(\frac{10 + 15 + 8}{120}\))

$12\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ = 12(\(\frac{33}{120}\))

= $12\left(\frac{1}{a}+\frac{1}{2 b}+\frac{1}{5 c}\right)$ =  $\frac{33}{10}$