Question

How many numbers are there between 101 and 999, which are divisible by both 2 and 5?

Answer 1

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

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 contain n terms. Then,

a_n = 990

⇒ 110 + (n – 1) × 10 = 990   ...[a_n  = a + (n – 1)d]

⇒ 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.