r proptional to a^2/b
if b => 2b
then a^2 needs to become 2a^2
so the new 'a' we need, lets call it 'A', should equal SQRT(2)

if thats not obvious you can try equations:
a^2/b = A^2/(2b)
A^2 = 2a^2
A=SQRT(2)*a

sqrt2 = 1.41 => 40% increase

Thanks a lot!

jason,

what happened to the "b"s ??

they cancel out.

jason,

When I cross-multiply I arrive at a^2 * 2b = A^2 * b

If you are dividing boths sides by b, you still end up with a b left over because you have a b on one side and 2b on the other.

you'll end up with 2 on one side and 1 on the other if you divide by b

you're thinking of subtraction.

Hi AleksandrM,
I think the following will remove your doubt:

R=k*A^2/B, where k=constant of proportionality.

Now when B is doubled, to keep the rate constant the numerator has to be multiplied with 2 which means an increase of A by sqrt2

Now, the increase in A=(1.4-1)=0.4*100=40%

Easy way to solve this problem is to plug in numbers

Assume
A = 10 and B = 5
A1 = ? and B1 = 10 (given a 100% increase)

The ratio stays the same. So,

A^2/ B = 100/5
A1^2 / B1 = A1^2/10

Solve for A1 which comes to 10* sqrt2

% Increase = (A1-A)/A * 100
= (sqrt2 -1) * 100
= 41% increase