A student is listing all the page numbers from 10 to 50 in her notebook. She wants to find the total of all the digits she has written while numbering these pages. What is the sum of all the digits used in writing the numbers from 10 to 50 (inclusive).
(a) 300
(b) 275
(c) 285
(d) 315

Question

A student is listing all the page numbers from 10 to 50 in her notebook. She wants to find the total of all the digits she has written while numbering these pages. What is the sum of all the digits used in writing the numbers from 10 to 50 (inclusive).
(a) 300
(b) 275
(c) 285
(d) 315

ONLiNE UPSC · Accepted Answer

Tens digits (10 &ndash; 50):
1 appears 10&times; &rarr; 10
2 &rarr; 10 &times; &rarr; 20
3 &rarr; 10 &times; &rarr; 30
4 &rarr; 10 &times; &rarr; 40
5 &rarr; 1 &times; &rarr; 5
Total = 10 + 20 + 30 + 40 + 5 = 105
Unit digits (0 &ndash; 9 repeated 4 times in 10 &ndash; 49):
Sum of 0 &ndash; 9 = 45 &rarr; 45 &times; 4 = 180
50 adds units digit 0 &rarr; +0
Final sum = 105 + 180 = 285

Hence option c is correct.

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M Question 1	⏱ 0
A student is listing all the page numbers from 10 to 50 in her notebook. She wants to find the total of all the digits she has written while numbering these pages. What is the sum of all the digits used in writing the numbers from 10 to 50 (inclusive). (a) 300 (b) 275 (c) 285 (d) 315