If, $$2^{x + y - 2z} = 8^{8z - 5 - y};5^{4y - 6z} = 25^{y + z};3^{4x - 3z} = 9^{x + z}$$ then the value of $$2x + 3y + 5z$$ is:

$$2^{x + y - 2z} = 8^{8z - 5 - y}$$

$$=$$>  $$2^{x+y-2z}=\left(2^3\right)^{8z-5-y}$$

$$=$$>  $$2^{x+y-2z}=2^{24z-15-3y}$$

$$=$$>  $$x+y-2z=24z-15-3y$$

$$=$$>  $$x+4y-26z=-15$$ ...................(1)

$$5^{4y - 6z} = 25^{y + z}$$

$$=$$>  $$5^{4y-6z}=\left(5^2\right)^{y+z}$$

$$=$$>  $$5^{4y-6z}=5^{2y+2z}$$

$$=$$>  $$4y-6z=2y+2z$$

$$=$$>  $$2y=8z$$

$$=$$>  $$y=4z$$ .........................................(2)

$$3^{4x - 3z} = 9^{x + z}$$

$$=$$>  $$3^{4x-3z}=\left(3^2\right)^{x+z}$$

$$=$$>  $$3^{4x-3z}=3^{2x+2z}$$

$$=$$>  $$4x-3z=2x+2z$$

$$=$$>  $$2x=5z$$

$$=$$>  $$x=\frac{5}{2}z$$ ........................................(3)

Substituting (2)  and (3) in (1)

$$=$$>  $$\frac{5}{2}z+16z-26z=-15$$

$$=$$>  $$\frac{5}{2}z-10z=-15$$

$$=$$>  $$10z-\frac{5}{2}z=15$$

$$=$$>  $$\frac{15}{2}z=15$$

$$=$$>  $$z=2$$

From (2),  $$y=4z=4\times2=8$$

From (3), $$x=\frac{5}{2}z=\frac{5}{2}\times2=5$$

$$\therefore\ $$ $$2x + 3y + 5z=2\left(5\right)+3\left(8\right)+5\left(2\right)=10+24+10=44$$

Hence, the correct answer is Option A