We blow one soap bubble with volume of air trapped ( say x) . We blow another bubble inside this bubble by blowing additional volume of air ( say y). So now the volume of air inside the first bubble is X + Y which is higher than x. But this additional volume does not make the size of the outer bubble change, it remains the same even when the second bubble inside is blown. why does this happen?
It's just an illusion. It does grow, but it's difficult to see.
Bubble in a Bubble is a youtube video that shows it pretty well. The outer bubble grows, but not obviously.
If we imagine a sphere with radius $R$ (the original bubble), and we want to put a new bubble inside with radius $R/2$, how big will the original bubble be? All we need to know is that it's proportional to the cube of the radius.
$$V = k R^3$$ $$V' = k R^3 + k (R/2)^3$$ $$V' = 1.125 k R^3$$ $$V' = k (1.04 R)^3$$
If you put a bubble inside that looks about half the size, the outer bubble radius only has to increase by 4% to accomodate. That's small enough to be difficult to see when not watching closely.