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UPSC Prelims 2023CSATQuantitative AptitudeNumber System - Sum of Digits

Q19. What is the sum of all digits which appear in all the integers from 10 to 100 ?

A. 855
B. 856✓ Correct
C. 910
D. 911

Detailed Solution

✓ Correct Answer: Option B

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.

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