Question

What percentage of numbers from $1$ to $70$ have squares that end in the digit $1$?

Answer 1

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 $=(\frac{14}{70}\times 100)=20\%$