Question

How many numbers are there between 987 and 1,087 which are divisible by 6?

Answer 1

The smallest number, which is greater than $987$ and divisible by $6$ is $990.$

The next number, which is divisible by $6$ is $990+6=996$ and so on.

Hence, numbers greater than $987$ and divisible by 6 can be represented as $990+6n\text{where}n\text{is a whole number}$

Largest number less than $1087$ and divisible by 6 is $1086$.

Numbers divisible by 6 are :
$990,\mathrm{996.....1086}$

To find the position of $1086$ in the series:
$\Rightarrow 990+6n=1086\Rightarrow 6n=1086-990=96\Rightarrow n=\frac{96}{6}=16$

Hence, first number greater than 990 is 996 and ${16}^{th}$ number greater than 990 is 1086.

There are $16$ muliplies of $6$ after $990$ and till $1087.$

Hence, including $990,$ there are $16+1=17$ multiples of $6$ between $987$ and $1,087.$