Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

The list of numbers between101and999that are divisible by2and5are:110,120,130,...990The numbers are in A.P, with first term,a=110, common difference,d=10Last term,an=990We know that,an=a+(n𕒵)d990=110+(n𕒵)10⇒990–110=10n–10⇒880+10=10n⇒890=10n⇒n=89Therefore, the number of terms between101and999that are divisible by2and5are89.