The numbers which are divisible by both 2 and 5 are divisible by 10 also.

Now, the numbers between 101 and 999 which are divisible 10 are 110,120,130,..,990.

Clearly, these number are in AP Here, a=110 and d=120−110=10

Let this AP contains n terms. Then,

a n =990

⇒110+(n−1)×10=990

⇒10n+100=990

⇒10n=990−100=890

⇒n=89

Hence, there are 89 numbers between 101 and 999 which are divisible by both 2 and 5.