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

Explanation : 

Sum of Digits of Intergers

Sum of the tens digits:

From 10 to 19, the tens digit is 1.
From 20 to 29, the tens digit is 2.
From 30 to 39, the tens digit is 3.
…
From 90 to 99, the tens digit is 9.
Each group contains 10 numbers.

Therefore, the sum of the tens digits is:
(1+2+3+4+5+6+7+8+9) x 10 = 45 x 10 = 450

Sum of the units digits:

The units digits from 10 to 100 repeat every ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
This sequence repeats 9 times (from 10 to 19, 20 to 29, …, 90 to 99).

Therefore, the sum of the units digits is:
(0+1+2+3+4+5+6+7+8+9) x 9 = 45 x 9 = 405

Adding the sums of tens and units digits:

450 + 405 = 855

However, we must also consider the number 100:
The tens digit is 10, and the units digit is 0.
The sum of digits in 100 is 1 + 0 + 0 = 1.

Adding this to our previous total:
855 + 1 = 856

Thus, the sum of all digits which appear in all the integers from 10 to 100 is 856. The correct answer is (b) 856.