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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
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B
200
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C
300
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D
280
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Solution

The correct option is B 200
5×(3,13,23,33,43,53,63,73,83,93)+5×(30,31,32,33,34,35,36,37,38,39)+(301,302,303,304,...,399)
=5×10+5×10+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.

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