Q. What is the sum of all digits which appear in all the integers from 10 to 100 ?
(a) 855
(b) 856
(c) 910
(d) 911
Correct Answer: (b) 856
Question from UPSC Prelims 2023 CSAT
Explanation :
Sum of Digits of Intergers
1) For numbers 10-99 (excluding 100):
Tens digits: Each digit (1 to 9) appears 10 times
Sum of tens digits = (1+2+3+4+5+6+7+8+9) × 10
Sum of tens digits = 45 × 10 = 450
2) Units digits: Each digit (0 to 9) appears 9 times
Sum of units digits = (0+1+2+3+4+5+6+7+8+9) × 9
Sum of units digits = 45 × 9 = 405
3) For number 100:
Sum of its digits = 1 + 0 + 0 = 1
4) Total sum = Sum of tens digits + Sum of units digits + Sum of digits in 100
Total = 450 + 405 + 1 = 856
Therefore, the sum of all digits which appear in all the integers from 10 to 100 is 856. The answer is (b) 856.