If all 7's are replaced by the digit 6 , then the number of 6's in series 1,2,3,4.....99, 100 will be (options)

Question

As the title says. The options available are:
(A) 31 (B) 32 (C) 33 (D) none of these

Thanks in advance. :)

Answer 1

Hint: in the collection of all integers you write, every number with two digits is represented (plus 100).

solution:

hence, the number of 6s is the same as the number of 7s, that is $10+10 =20$ (then for each spot, as $100$ does not count).

Then the answer is $40$ (none of these).

Answer 2

Hint

First, count the number of sixes in the series. We have 6, 16, 26, 36, ..., 96, as well as 60, 61, 62, ..., 69. Call this number $N$.

Second, cound the number of sevens in the series (in the same way, we have 7, 17, ..., 97, as well as 70, 71, ..., 79). Call this number $M$.

What would the sum $N+M$ be?