Question

If you write all the numbers from 201 to 250, then how many times will you write the numeral 2?
A.70
B.65
C.25
D.80

Answer 1

Hint: Here, we will first find the count of the numeral 2 in the first ten numbers, then in the second ten numbers, the third ten numbers, the fourth ten numbers and the last ten numbers. Then we will add all the count of numeral 2 to get the total number of numerals 2 from 201 to 250.

Complete step-by-step answer:
We have to find the total number of numerals 2 in the numbers from 201 to 250.
The number of times the numeral 2 occurs in the numbers 201 to 210 is 11, because the number 202 has the numeral 2 two times.
The number of times the numeral 2 occurs in the numbers 211 to 220 is 12, because the number 212, 220 has the numeral 2 two times.
The number of times the numeral 2 occurs in the numbers 221 to 230 is 20, because the number 222 has the numeral 2 three times and 230 has the numeral 2 one time.
The number of times the numeral 2 occurs in the numbers 231 to 240 is 11, because the number 232 has the numeral 2 two times.
The number of times the numeral 2 occurs in the numbers 241 to 250 is 11 because the number 242 has the numeral 2 two times.
Now, we will add all the occurrences of numeral 2 to get the total number of numerals 2 from 201 to 250.
Total number of numerals 2 from 201 to 250 $ = 11 + 12 + 20 + 11 + 11$
Adding the terms, we get
$ \Rightarrow $ Total number of numerals 2 from 201 to 250 $ = 65$
Therefore, the total times that the numeral 2 from the numbers 201to 250 is 65.
Thus, Option (B) is the correct answer.

Note: We can also calculate the total number by calculating the numeral 2 in the one’s place, ten’s place and hundredth’s place. The numeral 2 occurs five times in the one’s place, the numeral 2 occurs ten times and the numeral 2 occurs Fifty times in the hundredth’s place.
Thus, the total number of the numeral from the numbers 201 to 250 $ = 5 + 10 + 50 = 65$
Therefore, the total times that the numeral 2 from the numbers 201to 250 is 65.