Question

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

• A. $271$
• B. $272$
• C. $300$
• D. None of these

Answer 1

The correct option is C

$300$

Evaluate the number of times the given digit will appear between a given set of integers

Given integers, $1$ to $1000$

We know that the numbers having the digit $5$ from $1$ to $100$ are as follows,

$5$ at units digit $\to 5,15,25,35,45,55,65,75,85,95$

$5$ at tens digit $\to 50,51,52,53,54,55,56,57,58,59$

So, the number of times the digit $5$ is written from $1$ to $100=20$ [$\because 55$ has two $5$'s]

The same pattern would be followed in the numbers $101-200,201-300,301-400,401-500,501-600,601-700,701-800,801-900$ and $901-1000$.

Then, the number of times the digit $5$ is written as units and tens digit from $1$ to $1000=20\times 10$

$\Rightarrow$ $=200$

Again, as we know, the digit $5$ is written as hundreds digit from $500$ to $599$.

So, the number of times the digit $5$ is written as hundreds digit from $500$ to $599=100$

Thus, the total number of times the digit $5$ is written from $1$ to $1000=200+100$

$\Rightarrow$ $=300$

Hence, option (C) is the correct answer.