JMO STD V and STD VI

  

 Answer:

x1x = 100x + 10 + x
x2x = 100x + 20 + x
.
.
.
x9x = 100x + 90 + x

x1x + x2x +.... x9x = 9.100x + 10 ( 1+ 2 + ... 9) + 9x

x1x + x2x +.... x9x = 9.100x + 10. 9.10/2 + 9x

x1x + x2x +.... x9x = 9.100x + 450 + 9x

x1x + x2x +.... x9x = 9(100x + 50 + x)

So,( x1x + x2x +.... x9x) / x5x  = 9(100x + 50 + x) / (100x + 50 + x) = 9

Which is a perfect square