What percentage of numbers from 1 to 50 have 1 or 9 in the unit's digit?
20%
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 50 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49
Number of such numbers = 10
∴Required percentage=1050×100=20