The sum of x% of y and y% of z is z% of x. ........................................ satisfying the given condition.

Question

The sum of x% of y and y% of z is z% of x.
x and y are integers such that 1 = < x = < 9, 1 = < z = < 9.
If y is a perfect square number then how many ordered pair ( x , z ) are possible satisfying the given condition.

Answer 1

xy/100 + yz/100 = zx/100
y = xz/(x+z)
If either x or z is one then no possible case because n/(n+1) will never a perfect square.
For x=2 and z=2, y=1 (Perfect square)
Similarly for x=8 and z=8, y=4 (Perfect square)
For x=3 and z=9, sum=12
so y = 3*9/12 = 9/4 (Perfect square)
so (3,9) and (9,3) are possible pair
So total possible pairs are (2,2), (8,8), (3,9) and (9/3)
so answer is 4 ways