What is the sum of all digits which appear in all the integers from 10 to 100 ?

1. A. 855
2. B. 856
3. C. 910
4. D. 911

Answer: B

Explanation

We need to calculate the sum of all digits from 10 to 100.
1. For numbers from 10 to 99:
– Units digits: The digits 0, 1, 2, …, 9 each appear 9 times (e.g., 10, 20, …, 90 for 0; 11, 21, …, 91 for 1). The sum of digits from 0 to 9 is (9 * 10) / 2 = 45. So, the sum of all units digits is 9 × 45 = 405.
– Tens digits: The digits 1, 2, …, 9 each appear 10 times (e.g., 10-19 for 1; 20-29 for 2). The sum of digits from 1 to 9 is 45. So, the sum of all tens digits is 10 × 45 = 450.
– Total sum for numbers 10-99 = 405 (units) + 450 (tens) = 855.
2. For the number 100:
– The digits are 1, 0, 0. Their sum is 1 + 0 + 0 = 1.

Adding these two parts: Total sum of all digits from 10 to 100 = 855 + 1 = 856.