So the increase is 61c, and the percentage increase is 61/136 x 100 = 44.85%, as you said.
I have no idea where the factory is coming from - even if they did the calcualtion wrong and divided by the new price, it would still only be 30.96% (i.e., The old price is 30.96% lower than the new price).
Is it possible that one of you transposed digits on the original price? If the original was $1.63, then the increase is 24 cents, or 20.8% of the original price.
Or else whoever you’re talking to at the factory is an idiot. Either way.
This is a pet peeve of mine. Nobody seems to get percentages right. The problem is so pervasive that I never trust %age figures until I do the calculation myself.
Anyhow, I have no idea whence the 20% figure came. They must be using some really new math to come up with that one.