X is a two digit positive integer and Y is a three digit positive integer. If X is increased by Y% and Y is decreased by X%, they results same. How many solutio

Question

Can anyone please solve the problem below:

X is a two digit positive integer and Y is a three digit positive integer. If X is
increased by Y% and Y is decreased by X%, they results same. How many
solutions of (X, Y) are there for this case?

Answer 1

x + xy/100 = y - xy/100

 

This converts to:

 

y = 50x / (x - 50), x ≠ 0.

 

WolframAlpha.com indicates 30 integer values. Three that meet your requirements:

 

(-515, -46), (-450, -45), (-200, -40)