What percentage of numbers from 1 to 70 have squares that end in the digit 1 ?
The numbers from 1 to 70 that have their squares ending in digit 1 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 i.e. 14 in numbers
∴ Required percentage =(14/70)×100=20%
We will find the numbers whose unit digit is 1 or 9 because the numbers that end with 1 or 9 have their squares which end with 1 such as (1^2=1, 9^2=81).
So, from 1 to 10 there are only 2 numbers that end with 1 or 9. They are 1, 9.
Similarly, from 11 to 20. The numbers are 11 and 19.
From 21 to 30. The numbers are 21 and 29.
From 31 to 40 the numbers are 31 and 39.
From 41 to 50 the numbers are 41 and 49.
From 51 to 60 the numbers are 51 and 59.
From 61 to 70 the numbers are 61 and 69.
So, the total numbers that have 1 or 9
total at their unit places are 14.
Now,
(x/y×100)=(14/70)×100
=20%
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