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 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such numbers $=14$. ∴ Required percentage $=\left(\frac{14}{70} \times 100\right) \%=20 \%$.
Explanation as extracted from the printed page; notation may be imperfect.