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 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            [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.