Question

The number of natural numbers divisible by $5$ between $1$ and $1000$ is

• A. $197$
• B. $199$
• C. $198$
• D. $200$

Answer 1

Answer: (D)

$200$

There are $20$ numbers between$1$ to $100$ which are divisible by $5$

Thus, there are $20\times 10=200$ numbers between $1$ to $1000$ which are divisible by $5$.

OR

Let '$a$' be first multiple of $5=5$

'$n$' be the number of multiples between $1$ and $1000$.
'$d$' be the common difference $=5$
and $T$ be the last multiple between $1$ and $1000=1000$
$⟹$ $T=a+(n-1)d$ ......... (using A.P.)
$\therefore 1000=5+(n-1)5$
$995=(n-1)5$
$199=(n-1)$

$n=200$
Hence, there are $200$ numbers which are multiples of $5$ from $1$ to $1000$