The number of times the digit 5 will be written when listing the integers from 1 to 1000 is: -

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250

300

350

400

answer is B.

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Detailed Solution

We have to focus on numbers less than 1000 which can be formed by filling 3 empty block with 10 possible digits, repetition being allowed. We take 3 cases
1. When five is at the hundreds place, then there are 10×10 possible cases since the two other spaces can be filled with ten possible natural numbers each.
2. When five is at the tens place, again there are 10×10 possible cases since the first and the last place can be filled by ten possible numbers each time.
3. When five is at the unit’s place which again gives us 10×10 possibilities for the same reason.
Now we must note that for numbers like 555,550,505 we are supposed to count 3,2,2 respectively since 5 appears more than once in these numbers and the good news is that our method takes care of that automatically since a number like 505 will come twice, once when five is at the hundreds place and then again when five is at the unit’s place. Same thing happens with all such numbers so the final answer is 100+100+100 = 300.
Hence the correct option is 2.

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