What is the sum of all digits which appear in all the integers from 10 to 100?
- A855
- B856Correct
- C910
- D911
Explanation
To find the sum of all digits from 10 to 100, we break the range into two parts: 10 to 99 and the number 100.
First, consider numbers from 10 to 99. These are 90 two-digit numbers. The tens place contains the digits 1 through 9, each appearing 10 times. Sum of tens digits = 1+2+3+4+5+6+7+8+9 multiplied by 10 = 45 multiplied by 10 = 450.
The units place contains the digits 0 through 9, each appearing 9 times. Sum of units digits = 0+1+2+3+4+5+6+7+8+9 multiplied by 9 = 45 multiplied by 9 = 405.
Total sum for 10 to 99 = 450 + 405 = 855.
Finally, add the digits of the number 100. The digits are 1, 0, and 0. Their sum is 1.
Grand total = 855 + 1 = 856.
Therefore, the correct option is B.
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