Consider the following frequency distribution:

Class:	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	$a$	$b$	12	9	5

If mean $\frac{309}{22}$ and median $=14,$ then the value $2a+3b$ is equal to________.

Mean $\frac{504+3a+9b}{26+a+b}=\frac{309}{22}\Rightarrow 243a+111b=3054\Rightarrow 81a+37b=1018 \dots \dots \dots \left(i\right)$

Median class is 12 – 18 

Now, median $=12+\frac{\frac{a+b+26}{2}-(a+b)}{12}\times 6=14\Rightarrow \frac{a+b+26-2a-2b}{2}=4\Rightarrow a+b=18 \dots \dots \dots \dots . \left(ii\right)$

On solving eqs. (i) and (ii), we get $a=8,b=10$