Question

If x is increased by 10% and y is decreased by 20%, the resulting numbers will be equal. What is the ratio of x to y?

Answer 1

The equivalent of increasing a value by 10% is to mulitply it by 1.1, and to decrease by 20% is to multiply by .8. So we have:
\[1.1x=.8y\] The ratio of x to y is x/y, so rearrange to solve for x/y:
\[1=(.8y)/(1.1x)\] Multiply both sides by 1.1/.8
\[1.1/.8=y/x\] Flip both sides:
\[.8/1.1=x/y\] So the ratio of x to y is .8/1.1 or 8/11.