Question

When the natural numbers 1,2,3,..., 500 are written, then the digit 3 is used n times in this way. The value of n is:

• A. 100
• B. 200
• C. 300
• D. 280

Answer 1

The correct option is B 200

$5\times (3,13,23,33,43,53,63,73,83,93)+5\times (30,31,32,33,34,35,36,37,38,39)+(301,302,303,304,...,399)$
$=5\times 10+5\times 10+100=200$
Explanation: In every set of 100 numbers there are 10 numbers whose unit digit is 3. Similarly in every set of 100 numbers there are 10 numbers whose tens digit is 3 and there are total 100 numbers whose hundreds digit is 3.