Can someone explains it using algebra?

Let us assume the concentration of A as "A" and that of B as "B".

So if the rate is proportional to Square of the concentration of A and inversely proportional to the concentration of B, the rate equation is:

Rate = = k Square(A) / B, where k is a constant.

Now if the concentration of B is increased by 100%, it means B becomes 2B.

So new rate = k Square(A)/2B

Now in order to keep the concentration the same, in the above equation we have to multiply a 2 in the numerator. This can be achieved by making Square(A) as 2 x Square(A) - That is by increasing the concentration of A. If you make the concentration of A as SQrt(2) x A then the numerator becomes 2 x Square (A) and thus the rate will remain the same.

So in order to keep the same rate A should be INCREASED to SQrt(2) times A.

Square Root of 2 is approximately 1.414. So the new concentration of A is 1.41A which is approximately 40% increase in A.

Hope it helps.