CSAT 2023

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.

Check Demo Video

UPSC Factory

Master UPSC offline! 📚🎯 4000+ Prelims PYQs, Mains model answers, NCERT books, Syllabus tracker, topper notes, past papers.
Give it a try, you will love it !!💯

UPSC Factory for Android
Conquer UPSC offline! 🚀 PYQs (Prelims & Mains), Test Series, Syllabus Tracker.
Give it a try, you will love it 💯