PUZZLE-11

ANSWER : 4 numbers, they are 32,46,96,69.
SOLUTION:
Let 2 digits of number are x,y.
The given condition is
x+y=5(x-y);
x+y=5x-5y;
4x=6y;
x/y=3/2:
from the above condition we can get following pairs.
(x=3,y=2);(x=6,y=4);(x=9,y=6);
combinations of above pairs are 32,23,64,46,96,69.
in those numbers 64 is perfect square, 23 is prime number.
so the 2-digit numbers are 32,46,96,69.