I manipulated Quantity A and B by multiplying by 2 both sides and also accidentally got correct answer B , but a friend later told me its mathematically not allowed to perform that sort of operation
Why?
It is okay to perform operations on the Quantities, as long as it is the same operation applied on both the sides, and it is positive (if negative, then the comparison flips)
So, multiplying both sides by 2 is correct.