Question

What will be the percentage of numbers lying between 1 and 70 and had 1 or 9 at its unit’s digit ?
A. 1
B. 14
C. 20
D. 21

Answer 1

Hint: Unit’s digit is the right most digit of a number. So, let us find the total number having unit digit as 1 or 9. As we know that from 1 to 70 the total number of numbers is 70.

Complete step-by-step answer:
So, we had to find the total number of numbers in between 1 and 70 whose unit digit is 1 or 9.
As we know that from each 10 numbers starting from 1 we have one number which has unit digit equal to 1 and one number which has unit digit equal to 9.
Like from 1 to 10, 1 has unit digit as 1 and 9 has unit digit equal to 9.
In 11 to 20, 11 has unit digit 1 and 19 has unit digit 9. So, this goes on till 70.
So, we will get the set of numbers from 1 to 70 that has unit digit 1 or 9. And that set will be { 1, 9 , 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 } .
As we can see, the total number of numbers in this set is 14.
And we know that according to the percentage formula if B will be the total number then the percentage of A from a will be given as \[\dfrac{{\text{A}}}{{\text{B}}} \times 100\]%.
So, applying the percentage formula. We get,
\[\dfrac{{{\text{Total number of numbers between 1 and 70 whose unit digit is 1 or 9}}}}{{{\text{Total number of numbers between 1 and 70}}}} \times 100\] = \[\dfrac{{14}}{{70}} \times 100\] = 20%.
Hence, the percentage of numbers lying between 1 and 70 and had 1 or 9 at its unit digit will be 20%.
Hence the correct option will be C.

Note: Whenever we come up with this type of problem then first, we have to find total numbers without any condition and then we will find the number that follows the given condition like here unit in each 10 numbers from there are two numbers having unit digit as 1 or 9. After that we had to apply a percentage formula to get the required answer.