Question 363090
increase by 10% means you multiply by 1.10.


x + .10 * x = (1 + .10)*x = 1.10 * x
y + .10 * y = (1 + .10)*y = 1.10 * y


1.10 * (x + y) = 1.10 * x + 1.10 * y


your first ratio is x / (x + y)


your second ratio is 1.10x / 1/10 * (x + y)


you have a common factor of 1.10 which cancels out and you are left with x / (x + y)


since that's what you started with, the ratio becomes the same, i.e. there is a 0% change.


here's how it works.


assume x = 100 and y = 400


x / (x + y) = 100 / 500 = 1/5 = .2


increase both x and y by 10% to get:


x = 110 and y = 440


x + y = 110 + 440 = 550


take 110 / 550 = 1/5 = .2


the ratio is the same therefore the change in the ratio is 0.


if you look at 110 / 550, you will see that 110 = 100 * 1.1 and 550 = 500 * 1.10


if you take 1.10 * 100 / 1.10 * 500 you can see that the 1.10 in the numerator and in the denominator cancel out to get 100 / 500 which is what you started with.