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

The numbers which are divisible by both 2 and 5 are
110, 120, 130, 140 …..990.

The above numbers are in A.P. with common difference = d = 120 - 110 = 10 and first term = a = 110.

Last term = 990.

By formula, a_n = a + (n - 1)d

⇒ 990 = 110 + 10(n - 1)
⇒ 990 = 110 + 10n - 10
⇒ 990 = 100 + 10n
⇒ 990 - 100 = 10n
⇒ 10n = 890
⇒ n = 89.

Hence, there are 89 natural numbers between 101 and 999 that are divisible by 2 and 5.